ExamView - Test 4.1 - 4.3 review sheet.tst

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ID: A

4.1-4.3 Review sheet Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. A carousel with a 50-foot diameter makes 7 revolutions per minute. Find the angular speed of the

carousel in radians per minute. Round your answer to two decimal places. a. b. c. d. e.

7 rpm  56.85 radians per minute 7 rpm  43.98 radians per minute 7 rpm  65.97 radians per minute 7 rpm  21.99 radians per minute 7 rpm  43.23 radians per minute

Short Answer 2. Convert the angle measure from degrees to radians. Round to three decimal places.

0.63  3. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower a  110 feet

above the ground. The angle formed between the wire and the ground is   51 (see figure).

How long is the guy wire? Round your answer to one decimal place. 4. Given sin30 

3 1 and cos 30  , determine the following: 2 2

tan30

1

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5. Evaluate (if possible) the sine, cosine, and tangent of the real number.

t  3 6. Find the values of  in degrees (0    90 ) and radians (0     / 2) without the aid of a

calculator. 2 3

sec  

3

7. Find the values of  in degrees (0    90 ) and radians (0     / 2) without the aid of a

calculator. sin  

1 2

8. Use a calculator to evaluate function given below. Round your answer to four decimal places. (Be

sure the calculator is in the correct angle mode.) sec 4810 ' 9. Use the Pythagorean Theorem to determine the third side and then find the three trignometric

functions of  : sin  , cos  , and cot  tan  

3 4

10. Evaluate (if possible) the sine, cosine, and tangent of the real number.

t

19 3

11. Evaluate (if possible) the sine, cosine, and tangent of the real number.

t

7 2

2

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12. Find the exact values of the three trignometric functions of the angle  : sin , cos  and tan  of the

two triangles shown below. Is the function values are the same? Explain.

a 1  15, b 1  17

a 2  3.75, b 2  4.25

13. The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the

damping effect of friction is given by y(t) 

1

e t cos 6t , where y is the displacement (in feet) and t

4 is the time (in seconds). Complete the following table.(Round your answer to four decimal places.)

t

0

1

1

3

6

5

4

4

y 14. Evaluate the trigonometric function using its period as an aid.

sin

 4

15. Use the value of the trigonometric function to find sin t .

sin(t) 

3 2

3