ࡱ> 574 bjbj 4Rcc  zzzzzt~(~$s% zzzzz~~P'Зcj0, c  zl-   @: Exploring Sine and Cosine (Radians) y = a cos(b(x h)) + k Name: Directions: Go to  HYPERLINK "https://www.desmos.com/calculator" https://www.desmos.com/calculator (type in Desmos in your browser search). Type in the generic equation from above and click on All for the add sliders option when you are done typing. Please write all answers in sentence form. 1. Make sure the sliders are set with a = 1, b = 1, h = 0, k = 0. 2. What do you think will happen to the graph if you change the a slider? Put your prediction below: ___________________________________________________________________________________ Now change the a value by choosing the black arrow tool, grabbing the red vertical bar near a, and sliding it left and right. Was your prediction correct? _______ If no, describe what did happen below: __________________________________________________________________________________ 3. The AMPLITUDE of a sine or cosine is related to the height of the graph. It is (ymax ymin). Note: it is always a positive number. Fill in the table below: a-2-1-0.50.512ymaxyminamplitude How is the amplitude of the function related to the a value? ____________________________________________________________________________________ 4. What happens when you make a negative? ____________________________________________________________________________________ Reset a = 1, leave h and k at 0. We will now look at b. 5. The PERIOD of a trigonometric function is how long it takes to finish one cycle of the graph. What is the period of the parent function: y = sin(x)? ____________ 6. Use the slider to make b each of the values in the table below. Determine the period for each. b0.511.522.53Periodb*Period 7. How is the period related to the b value? ________________________________________________ 8. Write a formula for the period in terms of b (Hint: look at the last row and solve for b) Formula: _______________ Set a = 1, b = 1, h = 0, we will now look at k. The midline of a trig graph is the horizontal line that divides it into top/bottom. It is halfway between the ymin and ymax values. To find the midline, use the formula:  EMBED Equation.DSMT4 . 9. How is the midline changed as you change k? ___________________________________________ ___________________________________________________________________________________ 10. Fill in the table below: k-3-2-1012ymaxyminmidlineHow can you find the midline from the equation of the graph? _________________________________ ___________________________________________________________________________________ 11. What happens with multiple transformations? Fill in the following table: akamplitudemidlineyminymax21232-10.510.520.5-233313-3How could you find the ymin and ymax values from the midline and amplitude? __________________________________________________________________________________ __________________________________________________________________________________ 12. Use your answer to find the ymin and ymax values for the function y = 3 sin(x) + 4. Explain how you got your answer. Explore More Reset a = 1, b = 1, k = 0. 13. What happens when you change h? 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