Deck 5: Trigonometric Functions

Question 1

Given the figure below, determine the value of .

A) =
B) =
C) =
D) =
E) =

Answer 1

=

Question 2

Convert to degree-decimal form. Round answer to three decimal places.

A)
B)
C)
D)
E)

Answer 2

Question 3

If , find the value of $\theta$ in degrees without the aid of a calculator.

A)
B)
C)
D)
E)

Answer 3

Question 4

Rewrite in radian measure as a multiple of $\pi$ .

A)
B)
C)
D)
E)

Question 5

Find the radian measure of the central angle of the circle of radius 6 meters that intercepts an arc of length 32 meters.

A)
B)
C)
D)
E)

Question 6

Find (if possible) the supplement of .

A)
B)
C)
D)
E)not possible

Question 7

Find the length of the arc, S, on a circle of radius 4 inches intercepted by a central angle of . Round to two decimal places.

A) inches
B) inches
C) inches
D) inches
E) inches

Question 8

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 9

Determine the quadrant in which a ° angle lies.

A)3rd quadrant
B)4th quadrant
C)2nd quadrant
D)1st quadrant

Question 10

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 11

Find the angle, in radians, in the figure below if and .

A)
B)
C)
D)
E)

Question 12

Determine the quadrant in which a 141° angle lies.

A)1st quadrant
B)2nd quadrant
C)4th quadrant
D)3rd quadrant

Question 13

Using the figure below, if , determine the exact value of x.

A)
B)
C)
D)
E)

Question 14

Given and , determine the following.

A)
B)undefined
C)
D)
E)

Question 15

Rewrite in degree measure. Round to three decimal places.

A)
B)
C)
D)
E)

Question 16

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when , rounding answer to four decimal places.

A)-0.1892 cm
B)0.9370 cm
C)12.7373 cm
D)-2.1640 cm
E)2.1400 cm

Question 17

Find the area of the sector of the circle with radius 4 feet and central angle .

A)
B)
C)
D)
E)

Question 18

The point is on the terminal side of an angle in standard position. Determine the exact value of .

A)
B)
C)
D)
E)

Question 19

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 20

Determine the quadrant in which an angle, $\theta$ , lies if radians.

A)4th quadrant
B)1st quadrant
C)3rd quadrant
D)2nd quadrant

Question 21

Determine the quadrant in which an angle, $\theta$ , lies if radians.

A)2nd quadrant
B)1st quadrant
C)4th quadrant
D)3rd quadrant

Question 22

Convert to degree-decimal form. Round answer to three decimal places.

A)
B)
C)
D)
E)

Question 23

Rewrite in degree measure. Round to three decimal places.

A)
B)
C)
D)
E)

Question 24

Find the exact value of .

A)
B)
C)
D)
E)

Question 25

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 26

Find (if possible) the supplement of .

A)
B)
C)not possible
D)
E)

Question 27

Find the angle, in radians, in the figure below if and .

A)
B)
C)
D)
E)

Question 28

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

A)3.50
B)4.04
C)12.12
D)14.00
E)6.06

Question 29

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

A)
B)
C)
D)
E)

Question 30

Find the area of the sector of the circle with radius 2 feet and central angle .

A)
B)
C)
D)
E)

Question 31

After leaving the runway, a plane's angle of ascent is and its speed is 271 feet per second. How many minutes will it take for the airplane to climb to a height of 14,000 feet? Round answer to two decimal places.

A)2.26 minutes
B)0.90 minutes
C)0.86 minutes
D)1.57 minutes
E)2.94 minutes

Question 32

If , find the value of $\theta$ in degrees without the aid of a calculator.

A)
B)
C)
D)
E)

Question 33

Find the length of the arc, S, on a circle of radius 7 inches intercepted by a central angle of . Round to two decimal places.

A) inches
B) inches
C) inches
D) inches
E) inches

Question 34

Rewrite in radian measure as a multiple of $\pi$ .

A)
B)
C)
D)
E)

Question 35

Given and , determine the following.

A)
B)
C)undefined
D)
E)

Question 36

Find the radian measure of the central angle of the circle of radius 6 meters that intercepts an arc of length 32 meters.

A)
B)
C)
D)
E)

Question 37

Determine the quadrant in which a 174° angle lies.

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 38

Use an inverse function to write $\theta$ as a function of x.

A)
B)
C)
D)
E)

Question 39

Determine the quadrant in which a ° angle lies.

A)3rd quadrant
B)1st quadrant
C)2nd quadrant
D)4th quadrant

Question 40

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when , rounding answer to four decimal places.

A)2.8921 cm
B)-0.6329 cm
C)-2.8361 cm
D)1.7049 cm
E)-11.4839 cm

Question 41

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

A)13.33
B)8.92
C)10.80
D)17.93
E)16.15

Question 42

Find (if possible) the supplement of .

A)
B)
C)
D)
E)not possible

Question 43

Using the figure below, if , determine the exact value of x.

A)
B)
C)
D)
E)

Question 44

Determine the quadrant in which a 130° angle lies.

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 45

Use an inverse function to write $\theta$ as a function of x.

A)
B)
C)
D)
E)

Question 46

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 47

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 48

Determine the quadrant in which an angle, $\theta$ , lies if radians.

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 49

After leaving the runway, a plane's angle of ascent is and its speed is 266 feet per second. How many minutes will it take for the airplane to climb to a height of 14,500 feet? Round answer to two decimal places.

A)1.00 minutes
B)0.91 minutes
C)2.09 minutes
D)2.66 minutes
E)1.52 minutes

Question 50

Find the radian measure of the central angle of the circle of radius 5 feet that intercepts an arc of length 22 feet.

A)
B)
C)
D)
E)

Question 51

Find the exact value of .

A)
B)
C)
D)
E)

Question 52

Given the figure below, determine the value of .

A) =
B) =
C) =
D) =
E) =

Question 53

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

A)
B)
C)
D)
E)

Question 54

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 55

Rewrite in radian measure as a multiple of $\pi$ .

A)
B)
C)
D)
E)

Question 56

Convert to degree-decimal form. Round answer to three decimal places.

A)
B)
C)
D)
E)

Question 57

Find the angle, in radians, in the figure below if and .

A)
B)
C)
D)
E)

Question 58

Determine the quadrant in which a ° angle lies.

A)1st quadrant
B)2nd quadrant
C)3rd quadrant
D)4th quadrant

Question 59

Rewrite in degree measure. Round to three decimal places.

A)
B)
C)
D)
E)

Question 60

The point is on the terminal side of an angle in standard position. Determine the exact value of .

A)
B)
C)
D)
E)

Question 61

Determine the quadrant in which a ° angle lies.

A)4th quadrant
B)2nd quadrant
C)1st quadrant
D)3rd quadrant

Question 62

Find the exact value of .

A)
B)
C)
D)
E)

Question 63

Determine the quadrant in which an angle, $\theta$ , lies if .

A)3rd quadrant
B)4th quadrant
C)2nd quadrant
D)1st quadrant

Question 64

If , find the value of $\theta$ in degrees without the aid of a calculator.

A)
B)
C)
D)
E)

Question 65

Given the figure below, determine the value of .

A) =
B) =
C) =
D) =
E) =

Question 66

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 67

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

A)
B)
C)
D)
E)

Question 68

The point is on the terminal side of an angle in standard position. Determine the exact value of .

A)
B)
C)
D)
E)

Question 69

Determine two coterminal angles (one positive and one negative) for .

A)
B)
C)
D)
E)

Question 70

After leaving the runway, a plane's angle of ascent is and its speed is 267 feet per second. How many minutes will it take for the airplane to climb to a height of 12,500 feet? Round answer to two decimal places.

A)0.78 minutes
B)2.83 minutes
C)2.71 minutes
D)2.11 minutes
E)2.47 minutes

Question 71

Use an inverse function to write $\theta$ as a function of x.

A)
B)
C)
D)
E)

Question 72

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when , rounding answer to four decimal places.

A)2.7845 cm
B)-1.4973 cm
C)-5.8257 cm
D)-3.6205 cm
E)1.4460 cm

Question 73

Find the area of the sector of the circle with radius 4 centimeters and central angle .

A)
B)
C)
D)
E)

Question 74

Determine the quadrant in which a 118° angle lies.

A)1st quadrant
B)4th quadrant
C)2nd quadrant
D)3rd quadrant

Question 75

Find (if possible) the complement of .

A)
B)
C)not possible
D)
E)

Question 76

Find the length of the arc, S, on a circle of radius 7 feet intercepted by a central angle of . Round to two decimal places.

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

Question 77

Using the figure below, if , determine the exact value of x.

A)
B)
C)
D)
E)

Question 78

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 79

Given and , determine the following.

A)
B)
C)
D)
E)undefined

Question 80

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

A)10.29
B)16.24
C)18.56
D)4.99
E)4.36