Deck 5: Trigonometric Functions

Question 1

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Answer 1

Question 2

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

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

Answer 2

4th quadrant

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

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

A)
B)
C)
D)
E)

Question 5

Given the figure below, determine the value of .

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

Question 6

Determine the quadrant in which a ° angle lies.

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

Question 7

Find (if possible) the supplement of .

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

Question 8

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 9

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

A)
B)
C)
D)
E)

Question 10

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

A)
B)
C)
D)
E)

Question 11

Rewrite in degree measure. Round to three decimal places.

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

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

A)
B)
C)
D)
E)

Question 14

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 15

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 16

Evaluate without using a calculator.

A)
B)
C)
D)
E)

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

Given and , determine the following.

A)
B) undefined
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

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 21

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 22

Find the exact value of .

A)
B)
C)
D)
E)

Question 23

Determine the quadrant in which a 174° angle lies.

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

Question 24

Find (if possible) the supplement of .

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

Question 25

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 26

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

A)
B)
C)
D)
E)

Question 27

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

A)
B)
C)
D)
E)

Question 28

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

A)
B)
C)
D)
E)

Question 29

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 30

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

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

Question 31

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 32

Given and , determine the following.

A)
B)
C) undefined
D)
E)

Question 33

Determine the quadrant in which a ° angle lies.

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

Question 34

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 35

Rewrite in degree measure. Round to three decimal places.

A)
B)
C)
D)
E)

Question 36

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

A)
B)
C)
D)
E)

Question 37

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

A)
B)
C)
D)
E)

Question 38

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

A)
B)
C)
D)
E)

Question 39

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

A)
B)
C)
D)
E)

Question 40

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 41

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 42

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 43

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

A)
B)
C)
D)
E)

Question 44

Find the exact value of .

A)
B)
C)
D)
E)

Question 45

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 46

Determine the quadrant in which a 130° angle lies.

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

Question 47

Rewrite in degree measure. Round to three decimal places.

A)
B)
C)
D)
E)

Question 48

Find (if possible) the supplement of .

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

Question 49

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

A)
B)
C)
D)
E)

Question 50

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 51

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

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

Question 52

Given the figure below, determine the value of .

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

Question 53

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

A)
B)
C)
D)
E)

Question 54

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 55

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

A)
B)
C)
D)
E)

Question 56

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

A)
B)
C)
D)
E)

Question 57

Rewrite in degree measure.

A)
B)
C)
D)
E)

Question 58

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

A)
B)
C)
D)
E)

Question 59

Determine the quadrant in which a ° angle lies.

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

Question 60

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

A)
B)
C)
D)
E)

Question 61

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

A)
B)
C)
D)
E)

Question 62

Find the exact value of .

A)
B)
C)
D)
E)

Question 63

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

A)
B)
C)
D)
E)

Question 64

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

Question 65

Find (if possible) the complement of .

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

Question 66

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

A)
B)
C)
D)
E)

Question 67

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

A)
B)
C)
D)
E)

Question 68

Given and , determine the following.

A)
B)
C)
D)
E) undefined

Question 69

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

A)
B)
C)
D)
E)

Question 70

Determine the quadrant in which a 118° angle lies.

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

Question 71

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 72

Determine the quadrant in which a ° angle lies.

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

Question 73

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

A)
B)
C)
D)
E)

Question 74

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 75

Given the figure below, determine the value of .

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

Question 76

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 77

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 78

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

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

Question 79

Evaluate without using a calculator.

A)
B)
C)
D)
E)

Question 80

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

A)
B)
C)
D)
E)