Math 098 – Review for Midterm MOST of the test will allow ...

Math 098 ? Review for Midterm Here are some problems to practice for the midterm. In order to get full credit, YOU MUST SHOW PROCEDURES/REASONING - A correct answer without supportive work will give you only one point. You will lose ? pt for any missing unit. You will lose ? point for every rounding rule not respected. MOST of the test will allow a BASIC calculator (only +, -, x, division and sqrt keys) A second part to the test will be done with the GRAPHING/SCIENTIFIC calculator Section 6.1

1) Definitions of the six trigonometric functions 2) Given a triangle, give the trig functions of the acute angles

i) Sketch a right triangle, label one of the acute angles as A; the side opposite to A is 3 cm, the hypotenuse is 10 cm. Find all the trig functions of A.

3) Given the value of a trigonometric function, find reciprocal angle values. i) If sin A = 0.1234, find the reciprocal-function value rounded to four decimal places.

4) Know the values of the trigonometric functions of the angles 30, 60 and 45 degrees i) Give the exact values of all the trig functions of these angles.

5) Convert an angle from degrees to degrees, minutes and seconds i) 35.76 degrees to DMS -

6) Convert an angle from degrees, minutes and seconds to degrees i) 56 ? 35' 40" to Degrees -

7) Use the calculator to find the trig functions of acute angles. Show procedure.

i) Find cot 56 ?

csc 78 ?

sec46 ?

8) Use the calculator to find an acute angle to the nearest hundredth of a degree. i) tanA = 8.679 and A is in quadrant I, find the acute angle A in degrees

9) Relations between the trig functions of complementary angles (Functions = CO functions of the complement) 1. sin 54 ? = 0.809 = ...........(.......... ?)

2. cot 76 ? = 0.249 = .............(............. ?)

3. sec 81 ? = 6.392 = ..............(.......... ?)

10) Given one trigonometric function of an acute angle, find all other trig functions of the angle i) A is an acute angle, if sinA = 8/9, find all other trig functions. Rationalize denominator if needed

11) Solve right triangles: find all angles and sides of a right triangle i) In a right triangle the legs are 7cm and 8 cm. Find all sides and angles of the triangle ii) In a right triangle the hypotenuse is 15 cm and one of the acute angles is 23 ?. Find all other sides and angles.

Section 6.2 12) Solving right triangles ? applications 13) Solving right triangles involving angle of elevation 14) Solving right triangles involving angle of depression ? Know about angle of elevation and angle of depression o Read the problem, think on the situation o Sketch the right triangle that represents the situation o Label the sides of the triangle with the given info o Put x in the missing information in the graph o Think what trig function relates the given info with the missing info o Use that trig function to write the equation o Solve the equation i) Solve some problems from the book 15) Solving right triangles involving bearing

Section 6.3 16) Study the vocabulary Angle in standard position o Positive and negative rotation o Initial side o Terminal side o Coterminal angles o Reference angle o Supplementary angles o Quadrantal angles

17) Know the values of the trigonometric functions of quadrantal angles. Complete the table:

0?

90?

180 ?

270 ?

360 ?

450 ?

SINE

COSINE

TANGENT

540 ?

18) State in which quadrant is the terminal side of a given angle. Also, indicate which is the reference angle

i) a) 237 ?

b) -162 ?

c) 850 ?

d) -425 ?

19) Find two positive angles and two negative angles that are co-terminal to a given angle

i) a) 320 ?

b) -256 ?

20) Find the complement of an angle (do not transform to degrees, work with the given format of the angle) i) 46 ? 37'

21) Find the supplement of an angle i) 39 ? 52'

22) Given the coordinates of a point in the terminal side of an angle, find the six trigonometric function values for the angle i) P(-6, -7)

23) The terminal side of an angle in standard position lies on the line y = 2x, on the third quadrant. Find the trigonometric functions of the angle.

24) Sketch an angle in the correct quadrant and find the reference angle

25) Sketch an angle in the correct quadrant and determine the signs of trigonometric functions

i) a) cos 256 ?

b) sin ? 757 ?

26) Give the exact value of the trig functions of special angles in different quadrants without the calculator

i) sin 210 ?

ii) cos 300 ?

27) Find trigonometric functions of any angle ? with the calculator

i) cos 329 ?

ii) cot(31 ? 56')

28) Given the trig functions of a certain angle, find the trig functions of another i) In each problem, circle the correct statement a) sin 41 = sin 319 or sin 41 = - sin 319?

b) cos 32 = cos 212 or cos 32 = - cos 212?

c) tan 54 = tan 126 or tan 54 = - tan 126?

29) Given the value of a trig function of an angle and the quadrant in which the terminal side is, find all other trig functions i) tan A = 2/3 and the terminal side of A is in quadrant 3. Find all other trig functions of A

Section 6.4

30) Sketch a unit circle and mark the points determined by the given real numbers:

i) Pi/6

ii) pi/3

iii) pi

iv) 8pi

31) From a graph to a real number. Do problems 7 and 8 from the book, page 402

32) Convert from degrees to radian ? write exact answer in terms of pi

i) 125 ?

ii) 456 ?

33) Convert from degrees to radian ? round the answer to the nearest hundredth.

i) 345.2?

ii) 400?

34) Convert from radian to degrees i) a) (7pi/3) radians to degrees

b) 7.2 radians to degrees

35) Given the coordinates of a point on the unit circle, find all trig functions of the angle 26) P(-1/2, -(sqrt3)/2)

Section 6.5 36) Find the trig functions of an angle given in radians i) Without calculator a) Sin(4pi/3)

b) cos(-5pi/4)

c) tan(8pi)

d) cos(7pi/2)

ii) With calculator a) csc 3pi/7

b) cot 3.47

37) Use the calculator to find all angles within [0, 2p) satisfying the given condition

a) Sin x = 0.235

b) cos x = -0.87

c) cotx = 9.85

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