math 4

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1. Use a calculator to find the value of the expression below rounded to two decimal places.

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A. 44.42

B. 45.58

C. 0.80

D. 0.78

2. The point P (x,y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t.

Find sin t.

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3. Use a calculator to find the value of the expression below rounded to two decimal places.

sin–(0.7)

A. 0.80

B. 0.78

C. 44.43

D. 45.57

4. Use even and odd properties of the trigonometric functions to find the exact value of the expression:

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5. From a boat on a lake, the angle of elevation to the top of a cliff is 25°35'. If the base of the cliff is 1,325 feet from the boat, how high is the cliff (to the nearest foot)?

A. 634 feet

B. 644 feet

C. 647 feet

D. 637 feet

6. Find the exact value of the expression below. Do not use a calculator.

1 + sin280° + sin210°

A. –1

B. 2

C. 1

D. 0

7. Find the reference angle for the given angle below.

102°

A. 78°

B. 12°

C. 88°

D. 22°

8. Find the exact value of the expression below.

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9. Express the angular speed of 60 revolutions per second in radians per second.

A. 120 radians per second

B. 60π radians per second

C. 60 radians per second

D. 120π radians per second

10. Use reference angles to find the exact value of the expression below. Do not use a calculator.

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11. A rotating beacon is located 11 feet from a wall. If the distance from the beacon to the point on the wall where the beacon is aimed is given by a = 11|sec2πt|, where t is in seconds, find a when t = 0.38 seconds. Round your answer to the nearest hundredth.

A. 15.09 feet

B. 29.88 feet

C. 22.49 feet

D. –15.09 feet

12. Find the exact value of the expression, if possible. Do not use a calculator.

cos[cos–1(0.6)]

A. 0.8

B. 2.5

C. 0.6

D. 3.7

13. Find the exact value of the expression, if possible. Do not use a calculator.

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14. Convert the angle in radians to degrees:

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A. 1200π°

B. 300°

C. 10°

D. 600°

15. Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.

csc π

A. Undefined

B. 1

C. –1

D. 0

16. A car is traveling at 39 mph. If its tires have a diameter of 28 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

A. 468.19 revolutions per minute

B. 936.37 revolutions per minute

C. 2941.71 revolutions per minute

D. 449.19 revolutions per minute

17. An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and then released. Write an equation for the distance of the object from its rest position after t seconds.

amplitude = 17 cm period = 7 seconds

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18. Find the reference angle for an angle of 133°.

A. 53°

B. 57°

C. 43°

D. 47°

19. A building 240 feet tall casts a 40-foot-long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what's the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.)

A. 80.38°

B. 9.76°

C. 80.24°

D. 80.54°

20. Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators.

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Find csc t.

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