ࡱ> %&(0 !"#$%fMKLe S )` T4bjbj ,{{ e     ;.:- A A A B34gO:Q:Q:Q:Q:Q:Q:$=h@vu: u: A B>; A BO:O:Cf S B A fG+T;0;͓ @@ S@Spq-0]Qyu:u:";9D(D Math Analysis CP Algebra Review For each item, find or create a sample problem and then solve it. Graphs are to be neatly completed on graph paper. Given an algebraic relation, determine if it is a function. Given a function, state its domain and range. Given a function in function notation, evaluate it at a given value. Given two coordinate points, write the equation of the line that contains them. Given a linear function, determine its slope, x-intercept, and y-intercept. Given a horizontal or vertical line, determine its slope, intercepts, and graph. Given a direct variation, determine its slope, intercepts, and graph. Given an absolute value equation, determine its slope, intercepts, and graph. Given a quadratic function, determine the y-intercept, zeros, and graph. Given a rational function, determine the y-intercept, zeros, and excluded values. Given a linear function, find its inverse and graph both the original and inverse. Given two functions, find their composition  EMBED Equation.DSMT4 . --------------------------------------------------------------------------------------------------------- Math Analysis CP First Day of School You have two assignments to complete. They are due on Tuesday 9/6/16. Math Analysis Diagnostic Test Go to  HYPERLINK "http://defunct.mdtp.ucsd.edu/test_new/" http://defunct.mdtp.ucsd.edu/test_new/ Take the diagnostic test. You may use a calculator. Print the results and attach it to the assignment below. You only need to complete the test for full credit. This test is for your benefit to help find areas of weakness and is not graded on your actual score. Math Analysis Letter You will write me a letter that addresses the items listed below. The letter must be typed and free of spelling and grammatical errors. Each bullet should be well explained using at least one full paragraph. Tell me about your mathematical career. How did you get to this point? What has been your favorite math class? Why? How do you best learn math? What studying techniques have you utilized? What techniques have worked? Which techniques have not worked? Why? What grade do you hope to earn in this class? What are you going to do to achieve that goal? What is the one thing you want me to know about you? Math Analysis CP- Chapter 3A WS 3.2- Transformations of Graphs For each function, graph the parent function and the given transformation on the same coordinate grid.  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Describe how the graphs of  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4  are related.  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4   EMBED Equation.DSMT4 and  EMBED Equation.DSMT4  Write equations for the graphs of  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 , and  EMBED Equation.DSMT4  if the graph of  EMBED Equation.DSMT4 is the parent graph.  Math Analysis CP- Chapter 3A WS 3.1- Symmetry of Graphs Sketch each graph and determine whether it is symmetric with respect to the origin.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Determine if it is symmetric with respect to the x-axis, y-axis, the line y = x, or none of these.  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Sketch each function to determine if it is even, odd, or neither. Then prove your answer algebraically.  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Complete a sketch of the graph at right so that it is An odd function An even function Neither odd nor even Math Analysis CP- Chapter 3A WS 3.X- Families of Graphs Review What is a mathematical function? Draw a graph of a function that is (a) one-to-one, (b) many-to-one, and (c) a relation that is not a function. For each function below, graph the parent function and the given transformation on the same coordinate grid.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 State the domain and range of each graph in problem 2. Write the equations for the graphs of  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 , and  EMBED Equation.DSMT4  if the graph of  EMBED Equation.DSMT4 is the parent graph. Describe each transformation. Discuss the symmetry of the graph of  EMBED Equation.DSMT4 . Is  EMBED Equation.DSMT4  an even function, odd function, or neither? Prove your answer algebraically. Use three different methods to show that  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4  are inverses. To convert a temperature in degrees Fahrenheit (F) to degrees Celsius (C), you subtract 32 from F and multiply the quantity by 1.8. Write and graph an equation for C as a function of F. Find the inverse of your equation and graph it. Analysis CP- Chapter 5A WS 5A.1- The Unit Circle  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 09018027030120210300451352253156015024033090180270360 Analysis CP- Chapter 5A WS 5.2- Trig Chart Complete the chart with the exact values of the six trigonometric functions for the given angle measurements. RadianDegreesin cos tan csc sec cot 030456090120135150180210225240270300315330360MEMORIZE THE TRIG RATIOS FOR 0, 30, 45, 60, 90 Analysis CP- Chapter 5A WS 5.X- Chapter 5A Review Complete each problem without a calculator on a separate sheet of paper. Convert each angle measurement to a decimal degree measure. 2 revolutions clockwise b) -5745 c)  EMBED Equation.DSMT4  Find the exact values of the six trig functions if  EMBED Equation.DSMT4  Verify  EMBED Equation.DSMT4  Evaluate: a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  Solve for  EMBED Equation.DSMT4   EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4  Sketch each angle in standard position and give the measure of its reference angle a) -17 b) 185 c)  EMBED Equation.DSMT4  The terminal side of angle  lies in quadrant II and coincides with the line  EMBED Equation.DSMT4  a) Find  EMBED Equation.DSMT4  b) Find  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d) the reference angle If the central angle of a circle is 120 and the radius is 3, find a) the arc length b) the area of the sector You are riding a Ferris wheel with radius of 60 feet. You board the ride at the bottom of the wheel which is 5 feet off the ground. How far above the ground are you when the wheel has completed  EMBED Equation.DSMT4  rotations? Explain why the equation  EMBED Equation.DSMT4  must be true for all values of  EMBED Equation.DSMT4 . ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 5A WS 5.X- History of Trigonometry EC Answer the following questions with help from online sources. Type your answers in complete sentences. This is due the school day after the Chapter 05A Test. What is the origin of the word trigonometry? What branch of science first used trigonometry? Who is known as the father of trigonometry and approximately when did he live? Name one other ancient Greek who did early work with trigonometry and tell something he contributed. Name one Hindu (Indian) who did early work with trigonometry and tell something he contributed. Name one Islamic (Arab) who did early work with trigonometry and tell something he contributed. What did Leonhard Euler contribute to trigonometry? Give a brief explanation of the origins of the word sine. How were cosecant and secant defined? What does the prefix co mean in cosine, cosecant and cotangent? Math Analysis CP Name __________________________ Period _______ Sine/Cosine Parent Functions This page will help you review the graphs of the parent functions EMBED Equation.DSMT4and EMBED Equation.DSMT4, where x is measured in radian. You should complete this page without the aid of a graphing calculator. Use the unit circle to help evaluate the sine function y = sin(x) for values of x that are multiples of EMBED Equation.DSMT4 between EMBED Equation.DSMT4and EMBED Equation.DSMT4. Give exact values. x  EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 0 sin x  x  EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 sin x  Now use the ordered pairs to sketch a graph of y = sin(x). Note that the angle measure, x, is measured in radian.  Use your graph to answer the following questions about the sine function. Is the sine function periodic? ______________ What is its period? ________________ What is the domain of the sine function? ________________________________________ What is the range of the sine function? ________________________________________ Where are the x-intercepts located? __________________________________________ Where is the y-intercept? _____________________ What is the maximum value of the graph? ________ Where do the maximums occur? ____________________ What is the minimum value of the graph? ________ Where do the minimums occur?______________________  Use the unit circle to help evaluate the function y = cos(x) for values of x that are multiples of EMBED Equation.DSMT4 between EMBED Equation.DSMT4and EMBED Equation.DSMT4. Give exact values. x  EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 0 cos x  x  EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 cos x  Now use the ordered pairs to sketch a graph of y = cos(x). Note that the angle measure, x, is measured in radian.  Use your graph to answer the following questions about the cosine function. Is the cosine function periodic? _____________ What is its period? ________________ What is the domain of the cosine function? ______________________________________ What is the range of the cosine function? _______________________________________ Where are the x-intercepts located? __________________________________________ Where is the y-intercept? _____________________ What is the maximum value of the graph? ________ Where do the maximums occur? ____________________ What is the minimum value of the graph? ________ Where do the minimums occur?_____________________ We sometimes refer to the point on the graph where x = 0 as the starting point of the graph. What is the starting point of the cosine graph? _____________________ Of the sine graph? ________________________ Math Analysis CP Name __________________________ Period _______ Sine/Cosine Vertical Shift This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Be sure that your graphing calculator is in Radian mode. Set the graphing window to EMBED Equation.DSMT4. Equation D Graph using EMBED Equation.DSMT4Max valueMin valueEMBED Equation.DSMT41. EMBED Equation.DSMT42. EMBED Equation.DSMT43. EMBED Equation.DSMT44. EMBED Equation.DSMT45. EMBED Equation.DSMT4 Based on your investigation of D, answer the following questions.  1. A default value is the value in the parent equation,EMBED Equation.DSMT4. What is the default value of D? ______________ When EMBED Equation.DSMT4, what happens to the sine or cosine graph? _____________________________ When EMBED Equation.DSMT4, what happens to the sine or cosine graph? _____________________________ For periodic functions like the sine or cosine graph, the average value of the graph is given by EMBED Equation.DSMT4. What does the average value of EMBED Equation.DSMT4tell you about the graph? _________________________________ What is the centerline of the parent graphEMBED Equation.DSMT4 ? ________________________________________________ The graph of EMBED Equation.DSMT4has a new centerline because it has been shifted vertically from its original centerline, the x-axis. What is the equation of the new centerline? _________________________________________________ Write a formula for the centerline of EMBED Equation.DSMT4 in terms of D. _______________________________________ In general, what effect does D have on the graph of EMBED Equation.DSMT4or EMBED Equation.DSMT4? _______________________________________________________________________________________________ Graph each of the equations below without using a calculator. Then, check your answer on the calculator. EMBED Equation.DSMT4 b. EMBED Equation.DSMT4   Write an equation in the form EMBED Equation.DSMT4from the information given below. Maximum ValueMinimum ValueVertical ShiftEquation31-1-3422.50.5 Math Analysis CP Name __________________________ Period _______ Sine/Cosine Amplitude This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Be sure that your graphing calculator is in Radian mode. Set the graphing window to EMBED Equation.DSMT4. Equation A Graph using EMBED Equation.DSMT4Max valueMin valueEMBED Equation.DSMT41. EMBED Equation.DSMT42. EMBED Equation.DSMT43. EMBED Equation.DSMT44. EMBED Equation.DSMT45.EMBED Equation.DSMT4 Based on your investigation of A and D, answer the following questions. What is the default value of A? ___________________________ When EMBED Equation.DSMT4, what happens to the sine or cosine graph? _______________________________________________ When EMBED Equation.DSMT4, what happens to the sine or cosine graph? _______________________________________________ For periodic functions like the sine or cosine graph, the Amplitude of the function is given by EMBED Equation.DSMT4. What does the Amplitude of EMBED Equation.DSMT4 tell you about the graph? __________________________________ _______________________________________________________________________________________________ Are the graphs of EMBED Equation.DSMT4 and EMBED Equation.DSMT4symmetric? If so, to what line? ____________________ What overall effect does A have on the graphs of EMBED Equation.DSMT4and EMBED Equation.DSMT4. Be sure to include both the magnitude and sign of A. ______________________________________________________________________ _______________________________________________________________________________________________ Write formulas in terms of A and D for each of the quantities below. Remember that A and D can be positive or negative. Maximum value: ______________________________________________________ Minimum Value: ______________________________________________________ Amplitude: ___________________________________________________________ Equation of Centerline: _________________________________________________ Graph each of the equations below without using a calculator. Then, check your answer on the calculator. EMBED Equation.DSMT4 b. EMBED Equation.DSMT4   Write an equation in the form EMBED Equation.DSMT4from the information given below. MaximumMinimum AmplitudeVertical Shift Equation1-32-14-2-0.5-2.5 Write a cosine equation in the form EMBED Equation.DSMT4that increases over the interval EMBED Equation.DSMT4and has an amplitude between 1.0 and 2.0. _____________________________________________________________ Math Analysis CP Name __________________________ Period _______ Sine/Cosine Phase Shift This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Be sure that your graphing calculator is in Radian mode. Set the graphing window to EMBED Equation.DSMT4. Equation C Graph using EMBED Equation.DSMT4Amount and Direction of Phase Shiftx-intercepts 1. EMBED Equation.DSMT42. EMBED Equation.DSMT43. EMBED Equation.DSMT44. EMBED Equation.DSMT45. EMBED Equation.DSMT4 Based on your investigation of A, C and D, answer the following questions. 1. What is the default value of C? _______________________________ What overall effect does C have on the graphs of EMBED Equation.DSMT4and EMBED Equation.DSMT4? __________________________________________________________________________________________________ What effect does the sign of C have on the direction of the horizontal shift? ________________________________ __________________________________________________________________________________________________ What does C do to the x-intercepts of the graph? ____________________________________________________ __________________________________________________________________________________________________ Why is x-intercepts in quotes? (Hint: think about the graph when EMBED Equation.DSMT4) ________________________________ __________________________________________________________________________________________________ Based on your knowledge of the period, what would EMBED Equation.DSMT4look like? Why? _______________________ __________________________________________________________________________________________________ In the equation EMBED Equation.DSMT4, in what direction do A and D move the graph? _______________________ In what direction does C move the graph? _______________________________________________________________ We frequently call the point (0,0) the starting point of EMBED Equation.DSMT4. Why is starting point in quotes? __________________________________________________________________________________________________ What would be the starting point of EMBED Equation.DSMT4? _______________________________________________________ Which two of the three parameters A, C, and D control the starting point of the graph? _______________________ Graph each of the equations below without using a calculator. Then, check your answer on the calculator. EMBED Equation.DSMT4 EMBED Equation.DSMT4   EMBED Equation.DSMT4 EMBED Equation.DSMT4   Math Analysis CP Name __________________________ Period _______ Sine/Cosine Period This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Be sure that your graphing calculator is in Radian mode. Set the graphing window toEMBED Equation.DSMT4. Equation B Graph using EMBED Equation.DSMT4Number of Cycles in 2Length of One Cycle1. EMBED Equation.DSMT42. EMBED Equation.DSMT43. EMBED Equation.DSMT44. EMBED Equation.DSMT45. EMBED Equation.DSMT4 Based on your investigation of A, B, C, and D, answer the following questions. What is meant by Period with respect to sine and cosine graphs? _________________________________________ What is the default value of B in the parent functions, EMBED Equation.DSMT4andEMBED Equation.DSMT4? _________________________ When EMBED Equation.DSMT4, what is the period of the parent functions? _______________________________________________ How many cycles of the graph will you see between 0 and 2? ___________________________________________ When EMBED Equation.DSMT4, what happens to the period of the graph? ________________________________________________ What happens to the number of cycles between 0 and 2? ______________________________________________ When EMBED Equation.DSMT4, what happens to the Period of the graph? _____________________________________________ What happens to the number of cycles between 0 and 2? ______________________________________________ Write a formula that shows the relationship between B and the period of the graph (measured in radian). Remember that your formula must work for all the problems you have done. _______________________________ Rewrite the formula using degrees instead of radian. ___________________________________________________ Write an equation in the form EMBED Equation.DSMT4or EMBED Equation.DSMT4for each period. EMBED Equation.DSMT4____________________________________________ EMBED Equation.DSMT4___________________________________________ 12 ___________________________________________ Write a cosine equation whose graph has amplitude 2 and period EMBED Equation.DSMT4 ______________________________________ Write a sine equation whose graph has a vertical shift of -2, amplitude of 1.5, and period of EMBED Equation.DSMT4. _______________________________________________________________________________________________ Graph each of the equations below without using a calculator. Then, check your answer on the calculator. a.EMBED Equation.DSMT4 b. EMBED Equation.DSMT4   EMBED Equation.DSMT4 d. EMBED Equation.DSMT4   Math Analysis CP Name __________________________ Period _______ Sine/Cosine Graphs Based on your investigation, what overall effect does each have on the graphs of EMBED Equation.DSMT4 and EMBED Equation.DSMT4 A: _______________________________________________________________________________________________ B: _______________________________________________________________________________________________ C: ________________________________________________________________________________________________ D: _______________________________________________________________________________________________ Graph each of the following equations without a calculator. Then check your answers. EquationCenter- lineAmp- litudePeriodPhase Shift Graph EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 EquationCenter- lineAmp- litudePeriodPhase Shift Graph using EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4 Note that x is in degrees Write an equation of the form EMBED Equation.DSMT4for the information below. MaximumMinimumPeriodPhase ShiftEquation3 -2EMBED Equation.DSMT401-1EMBED Equation.DSMT4EMBED Equation.DSMT420EMBED Equation.DSMT40 1-3EMBED Equation.DSMT40 Math Analysis CP Name __________________________ Period _______ Sine/Cosine Graphs For each graph, determine the values of D, A, B and C. Then, write an equation in the formEMBED Equation.DSMT4 and EMBED Equation.DSMT4.  Sine Equation Cosine Equation1. A = B = CSin = CCos = D = 2. A = B = CSin = CCos = D =  3. A = B = CSin = CCos = D = 4. A = B = CSin = CCos = D =   Sine Equation Cosine Equation5. A = B = CSin = CCos = D =  6. A = B = CSin = CCos = D = 7. A = B = CSin = CCos = D =  8. A = B = CSin = CCos = D =   Math Analysis CP Name __________________________ Period _______ Tangent and Cotangent Graphs This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Recall that EMBED Equation.DSMT4 Graph EMBED Equation.DSMT4on your calculator. For what values of x does EMBED Equation.DSMT4? ______________________________________________ These values must be excluded from EMBED Equation.DSMT4. Why? ______________________________________________ The excluded values will be vertical asymptotes of the tangent graph. Draw them as dashed lines on the graph. Graph EMBED Equation.DSMT4on your calculator. Where does the sine graph cross the x-axis? ______________________ Why will the tangent graph cross the x-axis wherever the sine graph crosses it? _________________________ _______________________________________________________________________________________________ Draw the appropriate points on the graph above. Use you calculator to graph EMBED Equation.DSMT4. Sketch your graph above. Notice the relationship between your answers to (1) and (2) and to the tangent graph. Is the tangent graph periodic? _____________________ What is its period? ______________________________ Does the tangent graph have a maximum or minimum? _______________ If so, what are they? _______________ Does the tangent graph have a centerline? __________________ If so, what is it? _________________________ Why is centerline in quotes here? _________________________________________________________________  Use your calculator to graph EMBED Equation.DSMT4 and EMBED Equation.DSMT4 Where does the sine graph cross the line EMBED Equation.DSMT4? __________ Where does the tangent graph cross EMBED Equation.DSMT4? ______________ Compared to the graph of EMBED Equation.DSMT4, each point of EMBED Equation.DSMT4is shifted _____________________________ Overall, what effect does D have on the graph ofEMBED Equation.DSMT4________________________________________  Use your calculator to graphEMBED Equation.DSMT4. How does the graph compare to EMBED Equation.DSMT4? (Hint: you might want to look at the TABLE values) _________________________________________________ What effect does A have on the graph of EMBED Equation.DSMT4? _________________________________________________  Graph EMBED Equation.DSMT4 What effect does C have on the graph of EMBED Equation.DSMT4? _____________________________________________ Graph EMBED Equation.DSMT4 What is the period of the graph? __________________ Write a formula for the period of a tangent graph. ______________________________________________ Use your formula to predict the period of EMBED Equation.DSMT4 _____________________________________________ Check your prediction using the calculator. Were you correct? ___________ In general, do your concepts of A, B, C, and D for the sine graph hold true for the tangent graph? _______________  Recall that EMBED Equation.DSMT4 Where will the asymptotes of the cotangent graph be? ____________________________________________ Where will the graph cross x-axis? ____________________________________________ Use your calculator to draw a sketch of the cotangent graph. Sketch each of the equations below without a calculator. Then check your answers. Tangent GraphCotangent GraphEMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4Math Analysis CP Name __________________________ Period _______ Secant and Cosecant Graphs This page will help you investigate EMBED Equation.DSMT4and EMBED Equation.DSMT4. Recall that EMBED Equation.DSMT4 Graph EMBED Equation.DSMT4on your calculator. What values of x must be excluded from EMBED Equation.DSMT4. ______________________________________________ The excluded values will be vertical asymptotes of the secant graph. Draw them as dashed lines on the graph. Graph EMBED Equation.DSMT4on your calculator and on the graph above. Use you calculator to graph EMBED Equation.DSMT4 and EMBED Equation.DSMT4. What is the relationship between the maximum and minimum values of the cosine graph and the graph of EMBED Equation.DSMT4? _______________________________________ _______________________________________________________________________________________________ Is the secant graph periodic? _____________________ What is its period? _______________________________ Does the secant graph have relative maximums and minimums? __________________________________________ Why do we call the maximums and minimums relative? _______________________________________________  Use your calculator to graph EMBED Equation.DSMT4 and EMBED Equation.DSMT4 Could you have predicted the location of the asymptotes and relative maximums and minimums of the secant graph from the cosine graph? _________________________________ (If not, check that you have entered your equations correctly)  Use your calculator to graphEMBED Equation.DSMT4 and EMBED Equation.DSMT4 Could you have predicted the location of the asymptotes and relative maximums and minimums of the secant graph from the cosine graph? _____________________________________ Observe the graphs of EMBED Equation.DSMT4and EMBED Equation.DSMT4. Do your graphs agree with your predictions? _______ Observe the graphs of EMBED Equation.DSMT4and EMBED Equation.DSMT4. Do your graphs agree with your predictions? ____________ In general, the easiest way to graph EMBED Equation.DSMT4is to first graph the related _____________________ function.  Recall that EMBED Equation.DSMT4 Where will the asymptotes of the cosecant graph be? ____________________________________________ Where will the relative minimums and maximums be? ____________________________________________ Use your calculator to graph EMBED Equation.DSMT4and EMBED Equation.DSMT4  Use your calculator to sketch the graph of EMBED Equation.DSMT4. Use the sine graph to sketch EMBED Equation.DSMT4 Use your calculator to check that your cosecant graph is correct. In general, do your concepts of A, B, C and D from the sine and cosine graphs hold true for the secant and cosecant graphs? _______________________________________________________________________________________ Sketch each of the equations below without a calculator. Then check your answers. Secant GraphCosecant GraphEMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4 EMBED Equation.DSMT4 Math Analysis CP Name __________________________ Period _______ Review of Trig Graphs Complete the table below. Then graph each of the equations. 1. EMBED Equation.DSMT42. EMBED Equation.DSMT43. EMBED Equation.DSMT4PeriodHorizontal ShiftVertical ShiftAmplitudeMaximumMinimumDomainRangeNumber of cycles from 0 to 2Intervals from 0 to 2 where the graph is increasing    Math Analysis CP Name __________________________ Period _______ Review of Trig Graphs Complete the table below. Then graph each of the equations. 4. EMBED Equation.DSMT45. EMBED Equation.DSMT46. EMBED Equation.DSMT4PeriodHorizontal ShiftVertical ShiftAmplitudeMaximumMinimumDomainRangeNumber of cycles from 0 to 2Intervals from 0 to 2 where the graph is increasing    Math Analysis CP Extra Problems Extra Problems for WS 6.6 6-1. The equation  EMBED Equation.DSMT4  models the average monthly temperatures for Minneapolis, Minnesota. In this equation, t denotes the number of months with January represented by 1. What is the difference between the average monthly temperatures for July and January? What is the relationship between this difference and the coefficient of the sine term? What is the sum of the average monthly temperatures for July and January? What is the relationship between this sum and value of constant term? 6-2. The equation  EMBED Equation.DSMT4  models a persons blood pressure P in millimeters of mercury. In this equation, t is time in seconds. The blood pressure oscillates 20 millimeters above and below 100 millimeters, which means that the persons blood pressure is 120 over 80. This function has a period of 1 second, which means that the persons heart beats 60 times a minute. Find the blood pressure at  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 , and  EMBED Equation.DSMT4  During the first second, when was the blood pressure at a maximum? During the first second, when was the blood pressure at a minimum? 6-3. In predator-prey relationships, the number of animals in each category tends to vary periodically. A certain region has pumas as predators and deer as prey. The equation  EMBED Equation.DSMT4  models the number of pumas after t years. The equation  EMBED Equation.DSMT4  models the number of deer after t years. How many pumas and deer will there be in the region for each value of t? a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  ------------------------------------------------------------------------------------------------------------------------------------ Extra Problems for WS 6.7 7-1. A buoy in the harbor of San Juan, Puerto Rico, bobs up and down. The distance between the highest and lowest point is 3 feet. It moves from its highest point down to its lowest point and back to its highest point every 8 seconds. Find the equation of the motion for the buoy assuming that it is at its equilibrium point at  EMBED Equation.DSMT4  and the buoy is on its way down at that time. Determine the height of the buoy at 3 seconds. Determine the height of the buoy at 12 seconds. 7-2. The average monthly temperatures for Seattle, WA, are given below.  Find the amplitude of a sinusoidal function that models the monthly temperatures. Find the vertical shift of a sinusoidal function that models the monthly temperatures. What is the period of a sinusoidal function that models the monthly temperatures? Write a sinusoidal function that models the monthly temperatures, using  EMBED Equation.DSMT4  to represent January. According to your model, what is the average monthly temperature in February? How does this compare to the actual average? According to your model, what is the average monthly temperature in October? How does this compare to the actual average? ------------------------------------------------------------------------------------------------------------------------------------ Extra Problems for Extra Problems for WS 6.8 8-1. If a person has a blood pressure of 130 over 70, then the persons blood pressure oscillates between the maximum of 130 and a minimum of 70. Write the equation for the midline about which this persons blood pressure oscillates. If the persons pulse rate is 60 beats a minute, write a sine equation that models his or her blood pressure using t as time in seconds. Graph the equation. 8-2. In the wild, predators such as wolves need prey such as sheep to survive. The population of the wolves and the sheep are cyclic in nature. Suppose the population of the wolves W is modeled by  EMBED Equation.DSMT4 and population of the sheep S is modeled by  EMBED Equation.DSMT4  where t is the time in months. What are the maximum number and the minimum number of wolves? What are the maximum number and the minimum number of sheep? Use a graphing calculator to graph both equations for values of t from 0 to 24. During which months does the wolf population reach a maximum? During which months does the sheep population reach a maximum? What is the relationship of the maximum population of the wolves and the maximum population of the sheep? Explain. ------------------------------------------------------------------------------------------------------------------------------------ Extra Problems for WS 6.9 9-1. Write an equation for the given function given the period, phase shift, and vertical shift. tangent function, period =  EMBED Equation.DSMT4 , phase shift = 0, vertical shift = -6 cotangent function, period =  EMBED Equation.DSMT4 , phase shift =  EMBED Equation.DSMT4 , vertical shift = 7 secant function, period =  EMBED Equation.DSMT4 , phase shift =  EMBED Equation.DSMT4 , vertical shift = -10 cosecant function, period  EMBED Equation.DSMT4 , phase shift =  EMBED Equation.DSMT4 , vertical shift = -1 ------------------------------------------------------------------------------------------------------------------------------------ Extra Problems for WS 6.10 10-1. Write a sine equation that has the following information amplitude = 4, period =  EMBED Equation.DSMT4 , phase shift =  EMBED Equation.DSMT4 , and vertical shift = -1 amplitude = 0.5, period =  EMBED Equation.DSMT4 , phase shift =  EMBED Equation.DSMT4 , and vertical shift = 3 amplitude = 0.75, period =  EMBED Equation.DSMT4 , phase shift = 0, and vertical shift = 5 10-2 Suppose a persons blood pressure oscillates between the two numbers given. If the heart beats once every second, write a sine function that models this persons blood pressure. 120 and 80 130 and 100 10-3. The mean average temperature in a certain town is 64F. The temperature fluctuates 11.5 above and below the mean temperature. If  EMBED Equation.DSMT4  represents January, the phase shift of the sine function is 3. Write a model for the average monthly temperature in the town. According to your model, what is the average temperature in April? According to your model, what is the average temperature in July? ------------------------------------------------------------------------------------------------------------------------------------ Extra Problems for WS Review Day R-1. As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris Wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground. What is the lowest height of a seat? What is the equation of the midline? What is the period of the function? Write a sine equation to model the height of a seat that was at the equilibrium point heading upward when the ride began. According to the model, when will the seat reach the highest point for the first time? According to the model, what is the height of the seat after 10 seconds? R-2. If the equilibrium point is  EMBED Equation.DSMT4 , then  EMBED Equation.DSMT4  models a buoy bobbing up and down in the water. Describe the location of the buoy when  EMBED Equation.DSMT4 . What is the maximum height of the buoy? Find the location of the buoy at  EMBED Equation.DSMT4 . R-3. A certain persons blood pressure oscillates between 140 and 80. If the heart beats once every second, write a sine function that models the persons blood pressure. R-4. The initial behavior of the vibrations of the note E above middle C can be modeled by  EMBED Equation.DSMT4  What is the amplitude of this model? What is the period of this model? R-5. In a region with hawks as predators and rodents as prey, the rodent population R varies according to the model  EMBED Equation.DSMT4 , and the hawk population H varies according to the model  EMBED Equation.DSMT4 , with t measured in years since January 1, 1970. What was the population of rodents on January 1, 1970? What was the population of hawks on January 1, 1970? What are the maximum populations of rodents and hawks? Do these maxima ever occur at the same time? On what date was the first maximum population of rodents achieved? What is the minimum population of hawks? On what date was the minimum population of hawks first achieved? According to the models, what was the population of rodents and hawks on January 1 of the present year? R-6. A leaf floats on the water bobbing up and down. The distance between its highest and lowest point is 4 centimeters. It moves from its highest point down to its lowest point and back to its highest point every 10 seconds. Write a cosine function that models the movement of the leaf in relationship to the equilibrium point. R-7. The mean average temperature in Buffalo, New York, is 47.5. The temperature fluctuates 23.5 above and below the mean temperature. If  EMBED Equation.DSMT4  represents January, the phase shift of the sine function is 4. Write a model for the average monthly temperature in Buffalo. According to your model, what is the average temperature in March? According to your model, what is the average temperature in August? R-8. The average monthly temperatures for Honolulu, Hawaii, are given below.  Find the amplitude of a sinusoidal function that models the monthly temperatures. Find the vertical shift of a sinusoidal function that models the monthly temperatures. What is the period of a sinusoidal function that models the monthly temperatures? Write a sinusoidal function that models the monthly temperatures, using  EMBED Equation.DSMT4  to represent January. According to your model, what is the average temperature in August? How does this compare to the actual average? According to your model, what is the average temperature in May? How does this compare to the actual average? ------------------------------------------------------------------------------------------------------------------------------------ Math Analysis CP Ch 06 Extra Credit Extra Credit Problem This is due by Friday 10/7/16. It will not be accepted late, regardless of your attendance on or prior to the due date. You may turn it in early or have a friend submit it for you. It must be handed directly to the teacher, not placed in my mailbox in the office. It is worth a maximum of 5 points and completion does not necessarily guarantee any points. In this problem you will model the number of daylight hours each month in a city of your choice using data from  HYPERLINK "http://www.sunrisesunset.com" http://www.sunrisesunset.com. Your report must include: The name of your city. You must choose a city that begins with the first letter of your first or last name. (For example, Betty Smith might choose Bangkok or Shanghai). If the city you want is not on the list, you can go to the custom calendar page for even more city choices! A table showing the number of daylight hours each month for 12 consecutive months. You do not have to calculate the number of daylight hours for every day of the month; just do the first day of every month or the tenth day of each month or a day of your choice. Be sure to report which day youve chosen. Stay consistentif you choose the 5th of January, it must be the 5th for every month. A scatter plot of your data points with month on the x-axis and number of daylight hours on the y-axis. Your graph should be drawn on graph paper and be large enough to clearly show the data. A sinusoidal equation (both a sine and cosine equation) to model the data, including the work necessary to find the amplitude, frequency, phase shift, and vertical shift of the function. Your work must be visible. A sketch of your equation on the scatter plot. If you wish, this can be done on your calculator and you may print a screen capture. A prediction of the number of daylight hours in your city in the month and year of your graduation from high school. Thanks to Mrs. Grasel for the idea! Analysis CP- Chapter 5B WS 5B.5- Right Triangle Trigonometry Solve all problems neatly on a separate sheet of paper. Diagrams must be drawn and labeled. A man drives 500 feet along a road which is inclined 20 degrees to the horizontal. How high is he above his starting point? The base of a tree bent over by the wind forms a right angle with the ground. If the bent part of the tree makes an angle of 50 with the ground and if the top of the tree is now 20 feet high, how tall was the tree? Two straight roads intersect to form an angle of 75. Find the shortest distance from one road to a gas station on the other road 100 feet from the junction. Two buildings with flat roofs are 60 feet apart. From the roof of the shorter building, 40 feet in height, the angle of elevation to the edge of the roof of the taller building is 40. How high is the taller building? A ladder with its foot in the street makes an angle of 30 with the street when its top rests on a building on one side of the street and makes an angle of 40 with the street when its top rests on a building on the other side of the street. If the ladder is 50 feet long, how wide is the street? Find the perimeter of an isosceles triangle with a base of 40 inches and base angle of 70. Find the missing measures of the right triangles:   8. Give exact values for the lengths of all line segments (a e) and the measures of all angles (A-G) . Then find exact values for the sine, cosine and tangent of each angle. No calculators! Note: The figure is not drawn to scaleit never is!  Analysis CP- Chapter 5B WS 5B.7- Which Law For each triangle, (1) State the geometric theorem, (2) State which law (if any) could be used to solve the triangle, (3) Give the number of solutions and explain why. Do all work neatly on a separate sheet of paper.  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Select 5 (solvable) triangles from the above and give a complete solution. One angle of a rhombus is 3842 and its sides are 4.836 in. long. a) Find the length of the shorter diagonal. b) Find the area of the rhombus. The radius of a circle is 12 in. What is the measure of the central angle subtended by a chord 18 in. long? ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 5B WS 5B.X- Chapter 5B Review For problems #1-6, assume angles A, B, and C are opposite sides a, b, and c in  EMBED Equation.DSMT4  Given a = 5, b = 8, and C = 70, find c. Given c = 4, a = 6, and A = 50, find C. Given A = 3120, C = 6550 and c = 6, find b. Given b = 6, a = 5.5, and A = 64, find the area of  EMBED Equation.DSMT4 . Given c = 6, B = 6140, and A = 9230, find the area of  EMBED Equation.DSMT4 . Determine the number of triangles that exists and state the reason why. Then solve the triangle. If no triangle exists, give the reason why not. a) B = 40, b = 30, c = 20 b) B = 140, c = 30, b = 20 c) C = 5510, b = 480, c = 428 d) A = 60, a = 1.5, b = 2 e) A = 30, B= 60, C = 90 f) a = 10, b = 4, c = 5 The measures of the sides of  EMBED Equation.DSMT4 are in the ratio of 15:13:7. Find the measure of the largest angle. A triangular plot of ground has two sides 185 and 147 which intersect at an angle of 5110. Find the length of the third side and the area of the plot. Three circles with radii of 115 ft, 150 ft, and 225 ft. are tangent to each other. Draw the triangle formed by their centers. Find the measure of the three angles and the area of the triangle. A plane flying due east at 100 m/s is also being blown due south at 40 m/s by a strong wind. Find the speed and bearing of the plane (Bearing is measured from North, going clockwise). In Washington D.C. the Lincoln Reflecting Pool is due west of the Washington Monument. A tourist at the top of the Washington Monument sites the front edge of the Pool at an angle of depression of 27 and sites the far edge of the pool at an angle of depression of 10. If the Pool is 2030 feet long, about how high is the Washington Monument? ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Directions for the Chapter 5 Online Test Go to  HYPERLINK "http://www.amc.glencoe.com" www.amc.glencoe.com. Choose "Chapter Test" under "Chapter Resources". Then choose the Chapter 5 Test. Take the 16 question test and earn at least a 90%. You may retake the test until you earn a 90%. Once you earn at least a 90%, print the entire FIRST page of results showing your score at the top. The entire print job should be about four pages, but I only need the first one. Analysis CP- Chapter 7A WS Trig Identities 01- Algebra Review Section A: Factor the following completely.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Section B: Simplify the following completely.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Section C: Complete the square. Section D: Simplify the left side until it equals the right side.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 7A WS Trig Identities 02- Simplifying Completely simplify each problem. The answer to each problem will be one of the following:  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 , or 1.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 12.  EMBED Equation.DSMT4 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 7A WS Trig Identities 03- Proofs Prove the following. Use a two-column format, showing all work.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 10.  EMBED Equation.DSMT4  Analysis CP- Chapter 7A WS Trig Identities 04- Sum, Difference, and Double Angle Identities Section A: Simplify the following.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Section B: Prove each of the following.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 7A WS Trig Identities 05- Extra Practice Section A: Choose any 10 problems and prove the identity. Use a two-column format, showing all work.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Section B: Choose any 6 problems and prove the identity. Use a two-column format, showing all work.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Analysis CP- Chapter 7A WS Trig Identities 06- Review Prove each problem is an identity. Use a two-column format, showing all work.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Math Analysis CP- Chapter 7B WS 7.X- Evaluating Inverse Trig Functions For assistance, you may wish to look at Page 306 Example 1 or Page 345 Example 2 in your textbook. On a separate sheet of paper, complete the following: Give the degree measure(s), from  EMBED Equation.DSMT4 , for which the following expressions are true. Give the radian measure(s), from  EMBED Equation.DSMT4 , for which the following expressions are true.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 7B WS Solving Trigonometric Equations A Give the principal solution(s) for each equation. You must write an inverse equation and show algebraic support for every answer. Answer #1-8 in Radians and #9-16 in Degrees. Give exact solutions.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 7B WS Solving Trigonometric Equations B For problems #1-8, provide all real solutions (in Radian) for each equation. For #9-16, provide all solutions in the interval  EMBED Equation.DSMT4 . You must write an inverse equation and show algebraic support for every answer. Give exact solutions.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 7B WS Solving Trigonometric Equations C Solve each equation for principal values of x. Express solutions in degrees. Give exact values.Solve each equation for  EMBED Equation.DSMT4 . Give exact values.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Solve each equation for  EMBED Equation.DSMT4 . Give exact values.Solve each equation for  EMBED Equation.DSMT4 . Round your answers to the nearest thousandth. EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Solve each equation for all real values of x (in Radian). Give exact values. EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 7B WS Solving Trigonometric Equations D Write the equation for the inverse of each function. Then graph the function and its inverse on their own coordinate planes. Then state the domain and range of each.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Evaluate:  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Solve over the interval  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 09 WS 09- DeMoivre's Theorem Complete the following on a separate sheet of paper without a calculator. Write the polar form  EMBED Equation.DSMT4  of the point given the rectangular coordinates.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Find the rectangular form of the point with the given polar coordinates. Remember that a polar coordinate is of the form  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  Simplify.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Express each complex number in polar form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Express each complex number in rectangular form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Find each product or quotient. Then write the result in rectangular form.  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Find the following using DeMoivre's Theorem.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Solve the following using DeMoivre's Theorem.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Analysis CP- Chapter 09 Multiple Choice Review Simplify:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Simplify:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Simplify:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Express  EMBED Equation.DSMT4  in polar form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Express  EMBED Equation.DSMT4  in rectangular form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Simplify  EMBED Equation.DSMT4 and express the result in rectangular form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Simplify  EMBED Equation.DSMT4  and express the result in rectangular form.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Which of the following in not a root of  EMBED Equation.DSMT4  to the nearest hundredth?  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  For exercises 9-10, let  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . Write the rectangular form of  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Write the rectangular form of  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Math Analysis CP- Chapter 8 WS 8.1.1- Geometric Vectors Complete the following problems, neatly, on a separate sheet of paper.  Find the horizontal and vertical components of each vector above.  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A plane is flying due west at a velocity of 100 meters per second. The wind is blowing out of the north (to the south) at 5 meters per second. Draw a labeled diagram of the situation. What is the magnitude and direction of the plane's resultant velocity? Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy. The string makes an angle of 52 with the floor. Find the vertical and horizontal components of the force. If Belkis raises the string so that it makes a 78 angle with the floor, what are the magnitudes of the horizontal and vertical components of the force? Math Analysis CP- Chapter 08 WS 8.5- Vector Applications For each problem, make a sketch to show the given vectors and the resultant vector. Then solve the problem. Round magnitudes to the nearest hundredth and directions to the nearest tenth. DO NOT ROUND UNTIL THE FINAL ANSWER! Find the magnitude and direction of the resultant of a 425-newton force along the x-axis and a 390-newton force perpendicular to it. Find the magnitude and direction of the resultant of a 105-newton force along the x-axis and a 110-newton force at an angle of 50 to the first force. Two soccer players kick the ball at the same time. One players foot exerts a force of 70N west and the others foot exerts a force of 30 N south. Find the magnitude and direction of the resultant force on the ball. A hiker leaves camp and walks 13 km due north. The hiker then walks 15 km northeast (exactly midway between north and east). Find the hikers direction and displacement from her starting point. An airplane flies due west at 240 km/h. At the same time, the wind blows it due south at 70 km/h. Find the planes resultant velocity and direction. A pilot flies a plane east for 200 km, then 60 south of east for 80 km. Find the planes distance and direction from the starting point. 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hEhb+kCJEHOJQJU^JaJj<2X hb+kCJUVaJhb+kCJOJQJ^JaJ#jhb+kCJOJQJU^JaJ-j hEhb+kCJEHOJQJU^JaJ          . / 0 1 2 3 _ ` w x y z    ì䝆xfxW@fxfx-j. hl3hb+kCJEHOJQJU^JaJj2X hb+kCJUVaJ#jhb+kCJOJQJU^JaJhb+kCJOJQJ^JaJ-j2 hhthhtCJEHOJQJU^JaJj2X hhtCJUVaJ-j3 hhthhtCJEHOJQJU^JaJj2X hhtCJUVaJ#jhhtCJOJQJU^JaJhhtCJOJQJ^JaJhGCJOJQJ^JaJ  2 3   P y z      # $ % & C _ ` h^hgd>`gd>`gdt67gdb+k 7$8$H$gdvh^hgdvgdv & F0gdvgdG & F0gdGh^hgdht      O P x z   d e    " # $ % & 6 B C ^ ` ǹ~vn]L]L] hs~hBUCJOJQJ^JaJ hs~h>`CJOJQJ^JaJht67CJaJhhCJaJ hvhvCJOJQJ^JaJhvCJOJQJ^JaJhGCJOJQJ^JaJhvCJOJQJ^JaJhb+kCJOJQJ^JaJ#jhb+kCJOJQJU^JaJ-j% hl3hb+kCJEHOJQJU^JaJj2X hb+kCJUVaJ` BC`a;<$%hi !!T"""gdBUh^hgd>` & F, h^hgdBUgd>`` `a;<$%hi8Bx  !!R"T"""""### #~oX~-j# h")h>`CJEHOJQJU^JaJj8P h>`CJUVaJ#jh>`CJOJQJU^JaJ hs~h>`CJOJQJ^JaJ hs~hBUCJOJQJ^JaJhhCJOJQJ^JaJh>`CJOJQJ^JaJUhCJOJQJ^JaJ h")h>`CJOJQJ^JaJ h")h>`CJOJQJ^JaJ"  = 16.1 south of east (7)r = 220.49 lb,  = 33.3 (8) r = 155.24 km/h,  = 134.9 (east of north) (9) Area = 17.32 square units. 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Given A(-3, 7) and B(-4, 9) find: a) an ordered pair for  EMBED Equation.DSMT4  b) the magnitude of  EMBED Equation.DSMT4  c) the direction of  EMBED Equation.DSMT4  Given  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 : a) Find  EMBED Equation.DSMT4  b) Find  EMBED Equation.DSMT4  c) True or False?  EMBED Equation.DSMT4  Write each of the following vectors in the form ai + bj a) The vector joining the origin to P(2, -3) b) The vector joining P1(2, 3) to P2(4, 2) c) The vector joining P2(4, 2) to P1(2, 3) d) The vector having magnitude 6 and direction 120 Given  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find: a)  EMBED Equation.DSMT4  b) The sum of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  c) The dot product of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  d) The cross product of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  Determine if the vectors  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 are perpendicular. 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A B D E G H J K M N P Q S T V W Y Z \ ] _ ` b c e f             0 1 M N j k             00000. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 . 0 . 0 000000000000000 0 0 0 0000 00 0  0  0  0  0  0  0  0  0  0  00 00 0 0 0 000 00 0 0 0 0 0 000 00 0  0  0 00 00 0 0 0 000 00 0 0 0 00 0 00 0 0 0000 0 0 0 0 00 0 00 0 0 0 0 0  0 0 0 0 0 000000000000000000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000 0 0 0 00 00 0 00 00 000 000 0 0 0000000 0 0 0 0 0 0 0 0 0 0 0000000000 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00000 00 00 00 00 00 00 0000000 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 000000 00 00 00 00 00 00 00 0000000 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000 0 0 0 0 0 0 000 00 000 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 000 0 00 000000 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000 0 0 000 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0000 00 00 00 00 00 00 000 0 00000      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~000000000 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 000 0 000 00 00 0 0 0 0 0 0 0 00 0 000 000000 000000 000 00 00 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 00 00 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 000 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 000000 0 0 0 000 0 0 0 0000 0 0 0 00 0 0 0 000 0 0 0 0 000 000 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 00000000 00000000 00000 00 00000 0000000000 0000000 0000 00000000 00 0 0000000 0 0 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000000 00000 0 000 0000 00000000 000000 0 0 000 0 0000000 0 0000 0 0 0 00 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 0000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0 00000000000 000000000000 0000000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0 00000000000 000000000000 00000000000 0W 0W003 03 03 000000004 04 04 0000008 08 08 08 08 08 00000005 05 05 000 07 07 07 07 07 070000 0 0 0 00000; 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