Name: ________________________ Class: ___________________ Date: __________ ID: A

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Practice Test1 (1600 Trigonometry) Instructor: Koshal Dahal

Multiple Choice QuestionsSHOWALL WORK, EVEN FORMULTIPLE CHOICE QUESTIONS, TO RECEIVE CREDIT.

____ 1. Find the terminal point P (x, y) on the unit circle determined by t 132 . Round each value to the nearest

hundredth.a. (–0.00, –1.00)b. (0.00, 1.00)c. (0.00, –1.00)d. (0.12, 1.14)

____ 2. The point P is on the unit circle. The x-coordinate of P is 17 and P is in quadrant I. Find the point P(x, y).

a. 17 ,

487

b. 17 , 6

7

c. 17 ,

487

d. 17 ,

487

____ 3. The point P is on the unit circle. The x-coordinate of P is 27 and P is in quadrant II. Find the point P (x, y).

a. 27 ,

457

b. 27 ,

457

c. 27 , 5

7

d. 27 ,

457

Name: ________________________ ID: A

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____ 4. Find the terminal point P (x, y) on the unit circle determined by t 5 . Round the values to the nearest

hundredth.a. (0.93, 0.73)b. (0.81, –0.59)c. (–0.81, –0.59)d. (0.81, 0.59)

____ 5. Find the terminal point P (x, y) on the unit circle determined by t 4 . Round the values to the nearest

hundredth.a. (0.71, –0.71)b. (0.83, –0.85)c. (–0.71, 0.71)d. (–0.71, –0.71)

____ 6. Find the terminal point P (x, y) on the unit circle determined by t 56 . Round each value to the nearest

hundredth.a. (0.87, –0.50)b. (–0.87, –0.50)c. (–0.99, 0.64)d. (–0.87, 0.50)

____ 7. Suppose that the terminal point determined by t is 47 ,

337 . Find the terminal point determined by t .

a. 47 ,

337

b.337 , 4

7

c. 47 ,

337

d. 47 ,

337

Name: ________________________ ID: A

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____ 8. Find the reference number for t 54 .

a. 5

b. 54

c. 4

d. 4

____ 9. Find the terminal point P (x, y) and the reference number determined by t 23 . Round the coordinates of the

terminal point to the nearest hundredth, and express the reference number in terms of

a. terminal point is (–0.50, 0.87), reference number is 3

b. terminal point is (–0.50, –0.87), reference number is 3

c. terminal point is (0.50, –0.87), reference number is 3

d. terminal point is (0.50, 0.87), reference number is 23

____ 10. Find the terminal point P (x, y) and the reference number determined by t 56 . Round the coordinates of

the terminal point to the nearest hundredth, and express the reference number in terms of

a. terminal point is (0.87, –0.50), reference number is 6

b. terminal point is (–0.87, –0.50), reference number is 56

c. terminal point is (–0.87, –0.50), reference number is 6

d. terminal point is (–0.87, 0.50), reference number is 6

____ 11. Find the terminal point P (x, y) and the reference number determined by t 196 . Round the coordinates of

the terminal point to the nearest hundredth, and express the reference number in terms of

a. terminal point is (–0.87, 0.50), reference number is 6

b. terminal point is (–0.87, –0.50), reference number is 56

c. terminal point is (0.87, –0.50), reference number is 6

d. terminal point is (–0.87, –0.50), reference number is 6

Name: ________________________ ID: A

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____ 12. Find the terminal point P (x, y) and the reference number determined by t 616 . Round the coordinates of

the terminal point to the nearest hundredth, and express the reference number in terms of

a. terminal point is (–0.87, 0.50), reference number is 6

b. terminal point is (0.87, –0.50), reference number is 6

c. terminal point is (–0.87, –0.50), reference number is 56

d. terminal point is (–0.87, –0.50), reference number is 6

____ 13. Find the exact values of the trigonometric functions sin2 and cos 2 .a. sin2 1, cos 2 0b. sin2 1, cos 2 1c. sin2 0, cos 2 1

____ 14. Find the exact value of the trigonometric functions sin 132 and sin 11

2 .

a. sin 132 1, sin 11

2 0

b. sin 132 1, sin 11

2 1

c. sin 132 0, sin 11

2 1

____ 15. Find the exact values of the trigonometric functions sin 94 and cos 9

4 .

a. sin 94

32 , cos 9

43

2

b. sin 94

12 , cos 9

43

2

c. sin 94

22 , cos 9

42

2

____ 16. Find the exact values of the trigonometric functions sin 76 and sin 1

6 .

a. sin 76 0.5, sin 1

6 0.5

b. sin 76 0.5, sin 1

6 0.5

c. sin 76 0.5, sin 1

6 0.5

Name: ________________________ ID: A

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____ 17. Find the exact values of the trigonometric functions sec 133 and csc 7

3 .

a. sec 133 2, csc 7

32 3

3

b. sec 133 3, cot 7

3 2

c. sec 133 3, csc 7

33

3

____ 18. Find the exact values of the trigonometric functions sec 9 and csc 12 .

a. sec 9 1, csc 12 1

b. sec 9 1, csc 12 1

c. sec 9 1, csc 12

____ 19. Find the exact values of the trigonometric functions tan 54 and tan 11

4 .

a. tan 54

22 , tan 11

42

2

b. tan 54

32 , tan 11

43

2

c. tan 54 1, tan 11

4 1

____ 20. Find the exact value of the trigonometric function cos 152 .

a. cos 152 1

b. cos 152 0

c. cos 152 1

____ 21. The terminal point determined by t is 11 ,

01 . Find sin t, cos t, and tan t.

a. sin t 01 , cost 1

1 , tan t 01

b. sin t1

1 , cost 01 , tan t

01

c. sin t0

1 , cost 11 , tan t

01

Name: ________________________ ID: A

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____ 22. The terminal point determined by t is 34 ,

74 . Find sin t, cos t, and tan t.

a. sin t 74 , cost 3

4 , tan t 73

b. sin t3

4 , cost 74 , tan t

73

c. sin t7

4 , cost 34 , tan t

73

____ 23. Find the values of the trigonometric functions of t if sin t5

3 and the terminal point of t is in quadrant II.

a. sin t5

3 , cost 23 , tan t

52 , cot t

2 55

b. sin t5

3 , cost 23 , tan t 5

2 , cot t2 5

5

c. sin t5

3 , cost 53 , tan t

52 , cot t

2 55

____ 24. Find the values of the trigonometric functions of t if cost 610 and the terminal point of t is in quadrant III.

a. sin t64

10 , cost 610 , tan t

646 , cot t

6 6464

b. sin t64

10 , cost 610 , tan t

646 , cot t

6 6464

c. sin t64

10 , cost 610 , tan t

646 , cot t

6 6464

____ 25. Find the values of the trigonometric functions of t if sec t 11, and the terminal point of t is in quadrant IV.

a. sin t0

1 , cost 11 , tan t 0

1 , cot t1 0

0

b. sin t0

1 , cost 11 , tan t

01 , cot t

1 00

c. sin t0

1 , cost 01 , tan t

01 , cot t

1 00

Name: ________________________ ID: A

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____ 26. Find the values of the trigonometric functions of t if tan t 4 and the terminal point of t is in quadrant II.

a. sin t 624 , cost

54024 , tan t 4, cot t 1

4

b. sin t 624 , cost

54024 , tan t 4, cot t 1

4

c. sin t 624 , cost

54024 , tan t 4, cot t 1

4

____ 27. Find the values of the trigonometric functions of t if tan t115 and cos t 0.

a. sin t116 , cost 5

6 , tan t115 , cot t

5 1111

b. sin t116 , cost 5

6 , tan t115 , cot t

5 1111

c. sin t116 , cost 5

6 , tan t115 , cot t

5 1111

____ 28. Find the values of the trigonometric functions of t if sin t137 and sec t 0.

a. sin t137 , cost 13

7 , tan t136 , cot t

6 1313

b. sin t137 , cost 6

7 , tan t136 , cot t

6 1313

c. sin t137 , cost 6

7 , tan t 136 , cot t

6 1313

____ 29. Determine whether the function 9x2 cos x is even, odd, or neither.a. oddb. evenc. neither

____ 30. Determine whether the function |5x| cos 2x is even, odd, or neither.a. neitherb. oddc. even

Name: ________________________ ID: A

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____ 31. Graph the function.

g(x) 7cos x

a. d.

b. e.

c.

Name: ________________________ ID: A

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____ 32. Graph the function.

g(x) 6sinx

a. d.

b. e.

c.

Name: ________________________ ID: A

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____ 33. Graph the function.

g(x) 6 6cos x

a. c.

b. d.

Name: ________________________ ID: A

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____ 34. Graph the function.

g(x) 4 3sinx

a. d.

b. e.

c.

Name: ________________________ ID: A

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____ 35. Sketch the graph.

y 5cos 13 x

a. d.

b. e.

c.

Name: ________________________ ID: A

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____ 36. Find the period and graph the function.

y 2tanxa. period 2 d. period

b. period 2 e. period

c. period

Name: ________________________ ID: A

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____ 37. Find the period and graph the function.

y tan x 4

Name: ________________________ ID: A

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a. period 2 d. period

b. period e. period

c. period 2

Name: ________________________ ID: A

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____ 38. Find the exact value of sin 2 and cos 2 .

a. sin 2 0, cos 2 1

b. sin 2 1, cos 2 0

c. sin 212, cos 2

32

d. sin 2 1, cos 2 1

e. sin 2 1, cos 2 0

____ 39. Find the exact value of sec 74 and csc 17

4 .

a.2

3 , 23

b. 2, 12

c. 2, 2

d.2

2 , 2

e. 1, 1

____ 40. Find the exact value of the expression, if it is defined.

cos tan 1 3

a. 12

b.3

2c. 45

d. 12

e. none of these

Name: ________________________ ID: A

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____ 41. Find the approximate value of cos 1.8 using a calculator.

a. 0.14b. 0.23c. 0.69d. 0.51e. 0.85

____ 42. Find the exact value of the expression, if it is defined.

cot cos 1 22

a. 12

b. 45c. 1

d. 12

e. none of these

____ 43. Find the exact value of each expression, if it is defined.

sin 1 22

a. 3

b. 2

c. 4

d. 4

e. 3

Name: ________________________ ID: A

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Numeric Response

44. Find all solutions of the equation that lie in the interval 0, . State each answer correct to two decimal places.

cos x 0.9

x = __________

Short Answer

45. The point P is on the unit circle. Find P(x,y) from the given information.

The y-coordinate of P is 1011 and the x-coordinate is negative.

46. The point P is on the unit circle. Find P(x,y) from the given information.

The x-coordinate of P is positive and the y-coordinate of P is 10

10 .

47. Find the terminal point P(x,y) on the unit circle determined by the given value of t 43 .

48. Find the terminal point P(x,y) on the unit circle determined by the given value of t 53 .

Name: ________________________ ID: A

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49. Find the approximate value of the given trigonometric function.

sin1

(a) By using the figure. Please give the answer to one decimal place.

sin1 __________

(b) By using a calculator in radians. Please give the answer to five decimal places.

sin1 __________

50. Find all solutions of the equation that lie in the interval 0, . State each answer correct to two decimal places.

csc x 11

x = __________

Name: ________________________ ID: A

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51. Each time your heart beats, your blood pressure first increases and then decreases as the heart rests between beats. The maximum and minimum blood pressures are called the systolic and diastolic pressures, respectively. Your blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal.

A certain person's blood pressure is modeled by the function

p(t) 110 15sin(150 t)

where p(t) is the pressure in mmHg, at time t measured in minutes.

(a) Find the period of p.

period = __________ minute

(b) Find the number of heartbeats per minute.

(c) Find the blood pressure reading.

__________ / __________

(d) How does this compare to normal blood pressure?