Deck 10: Trigonometric Functions

Question 1

Determine the quadrant in which the angle lies.

A)Quadrant II
B)Quadrant I
C)Quadrant III
D)Quadrant IV

Answer 1

Quadrant I

Question 2

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in radians.

Answer 2

Question 3

Determine the quadrant in which the angle lies.

A)Quadrant II
B)Quadrant I
C)Quadrant III
D)Quadrant IV

Answer 3

Quadrant I

Question 4

Rewrite the given angle in degree measure. (Do not use a calculator.)

A)216°
B)138°
C)78°
D)123°
E)

Question 5

Convert the given angle measure from radians to degrees. Round to three decimal places.

A)0.012°
B)38.571°
C)77.143°
D)19.286°
E)840.000°

Question 6

Convert the angle measure to decimal degree form.

A)385.683°
B)386.019°
C)386.317°
D)6.737°
E)22,117.260°

Question 7

Find (if possible) the complement and supplement of the given angle.

A)
B)
C)
D)
E)

Question 8

Convert the angle measure to form.-233.855°

A)-233° 51'
B)-233° 51' 18"
C)-233° 855'
D)-233° 18' 51"
E)-233° 18'

Question 9

Sketch the angle in standard position.

A)
B)
C)
D)
E)none of these

Question 10

Convert the angle measure to decimal degree form.

A)346.478°
B)347.031°
C)347.522°
D)6.057°
E)19,884.558°

Question 11

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees.

Question 12

Sketch the angle in standard position.

A)
B)
C)
D)
E)none of these

Question 13

Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

A)IV
B)I
C)II
D)III
E)The angle lies on a coordinate axis.

Question 14

Determine the quadrant in which the angle lies. (The angle measure is given in radians.)

A)IV
B)I
C)II
D)III
E)The angle lies on a coordinate axis.

Question 15

Estimate, to the tens place, the number of degrees in the angle.

A)
B)
C)
D)
E)

Question 16

A three-inch-diameter pulley on an electric motor that runs at 1700 revolutions per minute is connected by a drive belt to a five-inch-diameter pulley that turns the mandrel on a woodworking lathe. Find the angular speed (in radians per minute) of each pulley.

A)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
B)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
C)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
D)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
E)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute

Question 17

Determine the exact value of .

A)
B)
C)
D)
E)

Question 18

Estimate the angle to the nearest one-half radian.

A)
B)
C)
D)
E)

Question 19

Rewrite the given angle in radian measure as a multiple of . (Do not use a calculator.)

A)
B)
C)
D)
E)

Question 20

Find the point (x, y) on the unit circle that corresponds to the real number t.

A)
B)
C)
D)
E)

Question 21

Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function. ; find

A)
B)
C)
D)
E)1

Question 22

Given that , find .[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]

A)
B)
C)
D)
E)

Question 23

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)

A)-0.3927
B)0.9583
C)0.4870
D)0.8734
E)1.1449

Question 24

Use the function value and constraint below to evaluate the given trigonometric function.Function Value Constraint Evaluate:

A)
B)
C)
D)
E)

Question 25

State the quadrant in which lies. < 0 and > 0

A)Quadrant II
B)Quadrant I
C)Quadrant IV
D)Quadrant III
E)Quadrant I or Quadrant III

Question 26

Given that , find .[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]

A)
B)
C)
D)
E)

Question 27

Using the figure below, determine the exact value of the given trigonometric function.

A)
B)
C)
D)
E)

Question 28

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

A)0.0183
B)0.5000
C)0.9998
D)1.1547
E)0.8660

Question 29

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

A)-0.0639
B)0.5000
C)0.9980
D)2.0000
E)-0.8660

Question 30

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

A)-0.0457
B)-0.8660
C)0.9990
D)-2.0000
E)-0.5000

Question 31

Evaluate, if possible, the given trigonometric function at the indicated value.

A)
B)
C)
D)
E)

Question 32

Evaluate the trigonometric function using its period as an aid.

A)
B)
C)
D)
E)

Question 33

Evaluate the trigonometric function using its period as an aid.

A)
B)
C)
D)
E)

Question 34

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

A)-0.0320
B)3.7321
C)0.9995
D)0.2679
E)-0.9659

Question 35

State the quadrant in which lies. > 0 and < 0

A)Quadrant I
B)Quadrant II
C)Quadrant III
D)Quadrant IV
E)Quadrant I or Quadrant III

Question 36

Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) a = 4

A)
B)
C)
D)1
E)

Question 37

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work.

Question 38

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)

A)0.2324
B)-0.0300
C)0.7716
D)0.6361
E)1.2131

Question 39

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)

A)1.0322
B)0.9449
C)1.0583
D)0.4756
E)0.3463

Question 40

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)

A)0.9568
B)-0.9291
C)-0.3698
D)2.5127
E)-2.7044

Question 41

Sketch the graph of the given function. Make sure to include at least two periods.

A)
B)
C)
D)
E)

Question 42

Determine the period and amplitude of .

A)period: ; amplitude:
B)period: ; amplitude:
C)period: ; amplitude:
D)period: ; amplitude:
E)period: ; amplitude:

Question 43

Which of the following functions is represented by the graph below?

A)
B)
C)
D)
E)

Question 44

Find two solutions of the equation in the interval . Give your answers in degrees.

A)
B)
C)
D)
E)

Question 45

Given the graph of f(x) below, sketch the graph of without the use of a graphing utility.

A)
B)
C)
D)
E)

Question 46

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.)

A)-0.9563
B)0.7958
C)0.4563
D)-0.2924
E)0.3057

Question 47

Sketch the graph of the given function. Make sure to include at least two periods.

A)
B)
C)
D)
E)

Question 48

Use a graphing utility to graph the function below. Be sure to include at least two full periods.

A)
B)
C)
D)
E)

Question 49

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.)

A)2.2812
B)-0.8988
C)1.0597
D)-1.1126
E)-0.4877

Question 50

Find a, b, and c for the function such that the graph of matches the graph below.

A)
B)
C)
D)
E)

Question 51

Use the function value and constraint below to evaluate the given trigonometric function.Function Value Constraint Evaluate:

A)
B)
C)
D)
E)undefined

Question 52

Describe the relationship between and . Consider amplitude, period, and shifts.

A)The period of g(x) is seven times the period of f(x).Graph of g(x) is shifted unit(s) relative to the graph of f(x).
B)The amplitude of g(x) is seven times the amplitude of f(x).Graph of g(x) is shifted unit(s) relative to the graph of f(x).
C)The period of g(x) is seven times the period of f(x).Graph of g(x) is shifted unit(s) relative to the graph of f(x).
D)The amplitude of g(x) is seven times the amplitude of f(x).Graph of g(x) is shifted unit(s) relative to the graph of f(x).
E)The period of g(x) is eleven times the period of f(x).Graph of g(x) is shifted unit(s) relative to the graph of f(x).

Question 53

Find the indicated trigonometric value in the specified quadrant.

A)
B)
C)
D)
E)undefined

Question 54

Given the graph of f(x) below, sketch the graph of without the use of a graphing utility.

A)
B)
C)
D)
E)

Question 55

Evaluate the tangent of the angle without using a calculator.

A)
B)
C)
D)
E)0

Question 56

Evaluate the cosine of the angle without using a calculator.

A)
B)
C)
D)
E)0

Question 57

Find the indicated trigonometric value in the specified quadrant.

A)
B)
C)
D)
E)undefined

Question 58

Sketch the graph of the function below, being sure to include at least two full periods.

A)
B)
C)
D)
E)

Question 59

Use a graphing utility to graph the function below. Be sure to include at least two full periods.

A)
B)
C)
D)
E)

Question 60

Find a and d for the function such that the graph of matches the graph below.

A)
B)
C)
D)
E)

Question 61

Use a graphing utility to graph the function below, making sure to show at least two periods.

A)
B)
C)
D)
E)

Question 62

Find the exact value of .

A)
B)
C)
D)
E)

Question 63

Find the exact value of .

A)
B)
C)
D)
E)

Question 64

Use the properties of inverse trigonometric functions to evaluate .

A)
B)
C)
D)
E)

Question 65

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 66

Use the graph shown below to determine if the function is even, odd, or neither.

A)
B)
C)

Question 67

If and , determine the value of c. Round to two decimal places.

A)9.01
B)8.64
C)11.12
D)5.67
E)4.41

Question 68

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 69

Use a graphing utility to graph the function. Describe the behavior of the function as x approaches 0.

A)
B)
C)
D)
E)

Question 70

The angle of elevation of the sun is . Find the length, l, of a shadow cast by a tree that is 47 feet tall. Round answer to two decimal places.

A) feet
B) feet
C) feet
D) feet
E) feet

Question 71

Use a graphing utility to graph the damping factor and the function in the same viewing window. Describe the behavior of the function as x increases without bound.

A)
B)
C)
D)
E)

Question 72

Determine which of the graphs below represents ^.

A)
B)
C)
D)
E)

Question 73

If and , determine the value of A. Round to two decimal places.

A)
B)
C)
D)
E)

Question 74

Use a graphing utility to graph the expression below, making sure to show at least two periods.

A)
B)
C)
D)
E)

Question 75

Use an inverse function to write as a function of x.

A)
B)
C)
D)
E)

Question 76

Use the properties of inverse trigonometric functions to evaluate .

A)
B)
C)
D)
E)

Question 77

Use a calculator to evaluate . Round your answer to two decimal places.

A)0.75
B)-0.63
C)0.94
D)-0.82
E)-0.67

Question 78

Use an inverse function to write as a function of x.

A)
B)
C)
D)
E)

Question 79

Use a graphing utility to graph the function below.

A)
B)
C)
D)
E)