MAC1114 Review Test 1 Version B PDF

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MAC1114 Trigonometry Study Guide Test 1 Review Version B (Chapter 9)

4𝜋

1. Find the complementary and supplementary angles to 11 . a. The complementary angle to the numerator.) b. The supplementary angle to numerator.)

4𝜋 11

4𝜋 11

is _______________ . (Simplify your answer. Write a fraction with π in

is _______________. (Simplify your answer. Write a fraction with π in the

2. Sketch the angle in standard position and draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle and closer to the given angle than any other coterminal angle. Give the quadrant of the angle, if applicable. A = − 62°

a. Choose the correct graph below, where the curve on each graph traces the angle beginning at the positive x-axis and ending at the ray.

o A.

o B.

o C.

b. The least positive coterminal angle is _______________ °. (Simplify your answer. Write an integer or a fraction.)

c. The greatest negative coterminal angle is _______________ °. (Simplify your answer. Write an integer or a fraction.)

d. When it is in standard position, the terminal side of A lies in which of the following quadrants. Select the correct choice below.

o A. Quadrant I o B. Quadrant II

o C. Quadrant III o D. Quadrant IV

o E. no quadrant

3. Convert the following radian measure to degree measure. 2𝜋 2𝜋 3

3

= _______________ °. 1 For worked out solution and video self-enroll: https://online.valenciacollege.edu/enroll/FR8BH9

2

4. How long is an arc intercepted by the given central angle in a circle of radius 16.81 ft? 30° The length of the intercepted arc is approximately _______________ ft. (Round to the nearest hundredth.)

5. The figure shows an angle θ in standard position with its terminal side intersecting the unit circle at 𝑃 (−

5 12 , ). Evaluate the circular functions 13 13

at θ. For each answer write an integer or a simplified fraction. a. sin θ = _______________ b. cos θ = _______________ c. tan θ = _______________

6. Find the trigonometric function values for 3π using the graph of the unit circle. Select the correct choices below and, if necessary, fill in the answer box(es) to complete your choice. For each answer simplify if necessary. a. Find sin 3π:

o A. sin 3π = _______________

o B. The function is undefined.

b. Find cos 3π:

o A. cos 3π = _______________

o B. The function is undefined.

c. Find tan 3π:

o A. tan 3π = _______________

o B. The function is undefined.

d. Find cot 3π:

o A. cot 3π = _______________

o B. The function is undefined.

e. Find sec 3π:

o A. sec 3π = _______________

o B. The function is undefined.

f. Find csc 3π:

o A. csc 3π = _______________

o B. The function is undefined. 12

7. Determine the values of the trigonometric functions of α, where sin α = − , and cos α = − 13 answer write a simplified fraction. a. tan α = _______________

c. sec α = _______________

b. csc α = _______________

d. cot α = _______________

5

. For each

13

2 For worked out solution and video self-enroll: https://online.valenciacollege.edu/enroll/FR8BH9

3

8. Choose the appropriate description of the following function. y = 3cos (7x - 5) Which of the following is the appropriate description of y = 3cos (7x - 5)?

o A. amplitude = 5, period = 27 π, phase shift = 3 o B. amplitude = 3, period = 72 π, phase shift = 5

o C. amplitude = 3, period = 72 π, phase shift = 75 o D. amplitude = 3, period = 27 π, phase shift = 75

9. Graph the following function over a two-period interval. Give the period and the amplitude. 1

y = sin x 6

1

a. What is the period of the function y = sin x? 6

_______________ (Simplify your answer. Write an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) 1 6

b. What is the amplitude of the function y = sin x? _______________ (Write an integer or simplified fraction.) 1

c. Which of the following is the correct graph of the function y = sin x? 6

o A.

o C.

o B.

o D. 3

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4

10. Graph the following function. y = 4 cos (𝑥 +

𝜋

10

)

Use the graphing tool to graph the function.

11. Find the graph of y = - 4 csc x. Choose the correct graph.

o A.

o B.

o C.

o D.

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5

12. Graph the function over a two-period interval. y = - 2 - tan x Choose the correct graph below.

o A.

o C.

o B.

o D.

13. Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (2, 0) is on the terminal side of θ. Then find the values of the six trigonometric functions for the angle. Rationalize denominators if applicable. Do not use a calculator. a. Choose the correct graph below.

o A.

o B.

o C.

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6

b. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. For each answer simplify if possible, including any radicals. Use integers or fractions for any numbers in the expression(s).

o A. sin θ = _______________ o A. cos θ = _______________ o A. tan θ = _______________ o A. csc θ = _______________ o A. sec θ = _______________ o A. cot θ = _______________

o B. The function is undefined. o B. The function is undefined. o B. The function is undefined. o B. The function is undefined. o B. The function is undefined. o B. The function is undefined.

14. Find the exact value of each of the remaining trigonometric functions of θ. 8

tan θ = − , given that θ is in quadrant II 15 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. For each answer simplify if possible, including any radicals. Use integers or fractions for any numbers in the expression(s).

o A. sin θ = _______________ o A. cos θ = _______________ o A. csc θ = _______________ o A. sec θ = _______________ o A. cot θ = _______________

o B. The function is undefined. o B. The function is undefined. o B. The function is undefined. o B. The function is undefined. o B. The function is undefined.

15. Find exact values or expressions for the six trigonometric functions of angle A. Do not use a calculator. For each answer write an integer or a simplified fraction. a. sin A = _______________

d. csc A = _______________

b. cos A = _______________

e. sec A = _______________

c. tan A = _______________

f. cot A = _______________

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7

16. Find the exact value of the following expression without using a calculator. cot 𝜋

𝜋 6

cot = _______________ (Simplify your answer, including any radicals. Use integers or fractions for any 6 numbers in the expression.)

𝜋

17. Find the exact value of csc . 3 𝜋

csc = _______________ (Simplify your answer, including any radicals. Use integers or fractions for any 3 numbers in the expression.)

18. Rewrite sin 72° in terms of its cofunction. sin 72° _______________ ° (Write an exact answer. Simplify your answer. Write any angle measured in degrees. Do not include the degree symbol in your answer.)

19. Find the reference angle of the angle. 7𝜋 4

The reference angle for

7𝜋 4

= _______________ . (Write your answer in radians. Write an exact

answer, using π as needed. Use integers or fractions for any numbers in the expression.)

20. Give the reference angle for angle measure −

4𝜋 3

.

The reference angle is _______________ . (Simplify your answer. Write an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)

21. Find the exact values of the six trigonometric functions of the angle. 1410° For each answer simplify. Write exact answers, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize any denominators. a. sin 1410° = __________

c. tan 1410° = __________

e. sec 1410° = __________

b. cos 1410° = __________

d. csc 1410° = __________

f. cot 1410° = __________

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8

22. Find the exact values of the six trigonometric functions for the angle −

3𝜋 4

by hand. Do not use a

calculator. For each answer simplify, including any radicals. Use integers or fractions for any numbers in the expression. a. sin (−

) = __________ 4

c. tan (−

3𝜋

3𝜋

d. cot (−

3𝜋

3𝜋

b. cos (−

4

) = __________

) = __________ 4 4

) = __________

e. sec (− f. csc (−

3𝜋

) = __________

4

3𝜋 4

) = __________

23. Use a calculator to find a decimal approximation for the following trigonometric function. sec 39°12’ sec 39°12’ ≈ _______________ (Simplify your answer. Write an integer or a decimal. Round to eight decimal places as needed.)

24. Solve the right triangle. a. Find the measure of M. M = _______________ . (Round to one decimal place as needed.) b. The length of side n = _______________ m and of side p = _______________ m. (Round to the nearest integer as needed.)

2

25. Suppose that you are headed toward a plateau 70 meters high. If the angle of elevation to the top of the plateau is 20°, how far are you from the base of the plateau? _______________ meters (Round to two decimal places as needed.)

8 For worked out solution and video self-enroll: https://online.valenciacollege.edu/enroll/FR8BH9

9

ANSWERKEY MAC1114 Test 1 Review Version B

1. a.

3𝜋 22

b.

7𝜋

12. C.

11

2. a. B. b. 298 c. -422 d. D.

13. a. C. b. A. sinθ = 0, A. cosθ = -1, A. tanθ = 0, B., A. secθ = -1, B.

3. 120

14. A. sinθ =

4. 8.80 5. a.

12

13

b. −

5

13

c. −

12

7. a.

12 5

b. −

13

12

c. −

8. D.

5 d. 12 5

13

17

, A. cosθ = −

A. secθ = −

5

6. a. A. 0 b. A. -1 c. A. 0 d. B. e. A. -1 f. B.

8

15. a.

28

53

b.

53

28

15

17

17

15

c.

, A. cscθ =

, A. cotθ = −

45

53

d.

53

45

e.

28

45

17 8

,

15

f.

8

45 28

16. √3 17.

9. a. 12π b. 1 c. C.

2√3 3

18. cos 18 19. 20.

𝜋 4 𝜋 3

1

21. a. − b. 2

22. a. −

√3 √3 c. − 3 2

√2 √2 b. − 2 2

d. −2 e.

2√3 3

f. −√3

c. 1 d. 1 e. −√2 f. −√2

23. 1.29041501 10.

24. a. M = 39.8 b. n = 150, p = 195

11. B.

25. 192.32

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