Deck 5: Trigonometric Functions

Question 1

Convert the angle to D° M' S'' form. Round the answer to the nearest second.

- $112.56 ^ { \circ }$

A) $112 ^ { \circ } 34 ^ { \prime } 36 ^ { \prime \prime }$
B) $112 ^ { \circ } 33 ^ { \prime } 56 ^ { \prime \prime }$
C) $112 ^ { \circ } 33 ^ { \prime } 36 ^ { \prime \prime }$
D) $112 ^ { \circ } 31 ^ { \prime } 56 ^ { \prime \prime }$

Answer 1

$112 ^ { \circ } 33 ^ { \prime } 36 ^ { \prime \prime }$

Question 2

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

- $$127 ^ { \circ } 58 ^ { \prime } 55 ^ { \prime \prime }$$

A) 128.04°
B) 127.94°
C) 127.99°
D) 127.98°

Answer 2

127.98°

Question 3

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.

- $\mathrm { r } = 15.3$ centimeters, $\theta = 3.5$ radians, $\mathrm { s } =$ ?

A) $55.6 \mathrm {~cm}$
B) $53.6 \mathrm {~cm}$
C) $52.6 \mathrm {~cm}$
D) $54.6 \mathrm {~cm}$

Answer 3

$53.6 \mathrm {~cm}$

Question 4

Draw the angle.

- $$- \frac { 7 \pi } { 6 }$$

A)

B)

C)

D)

Question 5

Draw the angle.

- $\frac { 7 \pi } { 4 }$

A)

B)

C)

D)

Question 6

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

- $$59 ^ { \circ } 6 ^ { \prime } 24 ^ { \prime \prime }$$

A) 59.11°
B) 59.12°
C) 59.17°
D) 59.07°

Question 7

Convert the angle to D° M' S'' form. Round the answer to the nearest second.

- $310.04 ^ { \circ }$

A) $310 ^ { \circ } 2 ^ { \prime } 24 ^ { \prime \prime }$
B) $310 ^ { \circ } 23 ^ { \prime } 4 ^ { \prime \prime }$
C) $310 ^ { \circ } 3 ^ { \prime 2 } 3 ^ { \prime \prime }$
D) $310 ^ { \circ } 2 ^ { \prime } 4 " ^ { \prime \prime }$

Question 8

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.

- $\mathrm { r } = 8.8 \text { inches, } \theta = 60 ^ { \circ } , \mathrm { s } =$ ?

A) 9.5 in.
B) 9.2 in.
C) 9.3 in.
D) 9.4 in.

Question 9

Draw the angle.

- $- 150 ^ { \circ }$

A)

B)

C)

D)

Question 10

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

- $$297 ^ { \circ } 20 ^ { \prime } 44 ^ { \prime \prime }$$

A) 297.35°
B) 297.31°
C) 297.41°
D) 297.36°

Question 11

Draw the angle.

-135°

A)

B)

C)

D)

Question 12

Draw the angle.

- $$- \frac { 3 \pi } { 4 }$$

A)

B)

C)

D)

Question 13

Draw the angle.

- $\frac { 5 \pi } { 3 }$

A)

B)

C)

D)

Question 14

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

- $$21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }$$

A) 21.22°
B) 21.29°
C) 21.34°
D) 21.37°

Question 15

Draw the angle.

-330°

A)

B)

C)

D)

Question 16

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

- $$23 ^ { \circ } 47 ^ { \prime } 37 ^ { \prime \prime }$$

A) 23.84°
B) 23.52°
C) 23.94°
D) 23.79°

Question 17

Draw the angle.

- $$\frac { 2 \pi } { 3 }$$

A)

B)

C)

D)

Question 18

Draw the angle.

-60°

A)

B)

C)

D)

Question 19

Convert the angle to D° M' S'' form. Round the answer to the nearest second.

- $64.64 ^ { \circ }$

A) $64 ^ { \circ } 38 ^ { \prime } 30 ^ { \prime \prime }$
B) $64 ^ { \circ } 38 ^ { \prime } 12 ^ { \prime \prime }$
C) $64 ^ { \circ } 38 ^ { \prime } 64 ^ { \prime \prime }$
D) $64 ^ { \circ } 38 ^ { \prime } 24 ^ { \prime \prime }$

Question 20

Draw the angle.

- $- 120 ^ { \circ }$

A)

B)

C)

D)

Question 21

Find the length s. Round the answer to three decimal places.

-

A) $4.084 \mathrm {~cm}$
B) $3.63 \mathrm {~cm}$
C) $4.992 \mathrm {~cm}$
D) $4.538 \mathrm {~cm}$

Question 22

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.

- $$\mathrm { r } = \frac { 1 } { 3 } \text { feet, } \mathrm { s } = 5 \text { feet, } \theta = \text { ? }$$

A) $\frac { 5 } { 3 } \circ$
B) 15 radians
C) $15 ^ { \circ }$
D) $\frac { 5 } { 3 }$ radians

Question 23

Solve the problem.
For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30°. Round to the nearest hundredth.

A) 6.28 ft
B) 4.19 ft
C) 376.99 ft
D) 2.09 ft

Question 24

Find the length s. Round the answer to three decimal places.

A) 10.996 yd
B) 5.498 yd
C) 1.795 yd
D) 8.913 yd

Question 25

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.

- $\mathrm { s } = 4.84 \text { meters, } \theta = 2.2 \text { radians, } \mathrm { r } =$ ?

A) 1.1 m
B) 2.2 m
C) 1.5 m
D) 0.45 m

Question 26

Choose the one alternative that best completes the statement or answers the question.
A pendulum swings though an angle of 20° each second. If the pendulum is 35 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places.

A) 13.51 in.
B) 12.22 in.
C) 10.37 in.
D) 14.65 in.

Question 27

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

-160°

A) $\frac { 7 \pi } { 8 }$
B) $\frac { 8 \pi } { 9 }$
C) $\frac { 9 \pi } { 10 }$
D) $\frac { 9 \pi } { 8 }$

Question 28

Convert the angle in radians to degrees.

- $$- \frac { 7 \pi } { 10 }$$

A) $- 125 ^ { \circ }$
B) $- 126 ^ { \circ }$
C) $- 127 ^ { \circ }$
D) $- 128 ^ { \circ }$

Question 29

Write the word or phrase that best completes each statement or answers the question.
Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt Lake City (40°45' north
latitude) and Flagstaff (35°16' north latitude). Assume that the radius of the Earth is 3960 miles. Round to
nearest whole mile.

Question 30

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

- $- 105 ^ { \circ }$

A) $- \frac { 7 \pi } { 12 }$
B) $- \frac { 6 \pi } { 11 }$
C) $- \frac { 12 \pi } { 7 }$
D) $- \frac { 8 \pi } { 13 }$

Question 31

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

--45°

A) $- \frac { \pi } { 5 }$
B) $- \frac { \pi } { 6 }$
C) $- \frac { \pi } { 4 }$
D) $- \frac { \pi } { 3 }$

Question 32

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

- $87 ^ { \circ }$

A) $\frac { 29 \pi } { 120 }$
B) $\frac { 29 \pi } { 90 }$
C) $\frac { 29 \pi } { 30 }$
D) $\frac { 29 \pi } { 60 }$

Question 33

Find the length s. Round the answer to three decimal places.

-

A) $7.54 \mathrm { ft }$
B) $2.618 \mathrm { ft }$
C) $9.549 \mathrm { ft }$
D) $3.77 \mathrm { ft }$

Question 34

Choose the one alternative that best completes the statement or answers the question.
The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places.

A) 27.06 in.
B) 28.8 in.
C) 31.31 in.
D) 30.03 in.

Question 35

Find the length s. Round the answer to three decimal places.

-

A) $3.84 \mathrm {~m}$
B) $2.793 \mathrm {~m}$
C) $3.491 \mathrm {~m}$
D) $3.142 \mathrm {~m}$

Question 36

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

-30°

A) $\frac { \pi } { 8 }$
B) $\frac { \pi } { 6 }$
C) $\frac { \pi } { 7 }$
D) $\frac { \pi } { 5 }$

Question 37

Convert the angle in radians to degrees.

- $$\frac { 12 \pi } { 3 }$$

A) $720 ^ { \circ }$
B) $719 ^ { \circ }$
C) $722 ^ { \circ }$
D) $721 ^ { \circ }$

Question 38

Solve the problem.
A ship in the Atlantic Ocean measures its position to be 30°48' north latitude. Another ship is reported to be due north of the first ship at 41°17' north latitude. Approximately how far apart are the two ships? Round to the
Nearest mile. Assume that the radius of the Earth is 3960 miles.

A) 725 mi
B) 75,966 mi
C) 75,991 mi
D) 1,351 mi

Question 39

Solve the problem.
For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60°. Round to the nearest hundredth.

A) 4.25 ft
B) 4.40 ft
C) 4.19 ft
D) 4.35 ft

Question 40

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$

- $$6 ^ { \circ }$$

A) $\frac { \pi } { 15 }$
B) $\frac { \pi } { 18 }$
C) $\frac { \pi } { 30 }$
D) $\frac { \pi } { 60 }$

Question 41

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $\mathrm { r } = 9$ feet, $\mathrm { A } = 39$ square feet, $\theta =$ ?

A) $0.48$ radians
B) 3,159 radians
C) $0.96$ radians
D) $1,579.5$ radians

Question 42

Convert the angle in radians to degrees.

- $$- \frac { 23 } { 9 } \pi$$

A) $- 920 \pi ^ { \circ }$
B) $- 230 ^ { \circ }$
C) $- 8 ^ { \circ }$
D) $- 460 ^ { \circ }$

Question 43

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places.

- $$\sqrt { 7 }$$

A) 0.05°
B) 151.59°
C) 151.47°
D) -0.04°

Question 44

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $\mathrm { r } = 5$ inches, $\theta = 2$ radians, $\mathrm { A } =$ ?

A) $25 \mathrm { in } ^ { 2 }$
B) 50 in 2
C) 10 in 2
D) 5 in $^ { 2 }$

Question 45

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places.

- $- 308 ^ { \circ }$

A) $- 5.37$
B) $- 5.36$
C) $- 5.38$
D) $- 5.35$

Question 46

Convert the angle in radians to degrees.

- $\frac { \pi } { 6 }$

A) $1080 ^ { \circ }$
B) $60 ^ { \circ }$
C) $30 ^ { \circ }$
D) $15 ^ { \circ }$

Question 47

Convert the angle in radians to degrees.

- $\frac { 11 \pi } { 12 }$

A) $150 ^ { \circ }$
B) $210 ^ { \circ }$
C) $160 ^ { \circ }$
D) $165 ^ { \circ }$

Question 48

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places.
6.46

A) 0.11°
B) 370.13°
C) 0.22°
D) 369.26°

Question 49

Convert the angle in radians to degrees.

- $\frac { 7 \pi } { 12 }$

A) $154 ^ { \circ }$
B) $309 \pi ^ { \circ }$
C) $105 ^ { \circ }$
D) $210 ^ { \circ }$

Question 50

Find the area A. Round the answer to three decimal places.

-

A) $1.963 \mathrm {~m} ^ { 2 }$
B) $9.817 \mathrm {~m} ^ { 2 }$
C) $6.25 \mathrm {~m} ^ { 2 }$
D) $19.635 \mathrm {~m} ^ { 2 }$

Question 51

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places.

- $353 ^ { \circ }$

A) $6.13$
B) $6.14$
C) $6.16$
D) $6.15$

Question 52

Convert the angle in radians to degrees.

- $- \frac { \pi } { 5 }$

A) $1 ^ { \circ }$
B) $- 36 ^ { \circ }$
C) $- 1 ^ { \circ }$
D) $- 36 \pi ^ { \circ }$

Question 53

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $r = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $A =$ ?

A) $176.8 \mathrm {~cm} ^ { 2 }$
B) $56.3 \mathrm {~cm} ^ { 2 }$
C) $4.5 \mathrm {~cm} ^ { 2 }$
D) $353.6 \mathrm {~cm} ^ { 2 }$

Question 54

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta = ?$

A) $14.86 ^ { \circ }$
B) $1,560,152.87 ^ { \circ }$
C) $29.72 ^ { \circ }$
D) $780,076.43 ^ { \circ }$

Question 55

Convert the angle in radians to degrees.

- $$\frac { \pi } { 5 }$$

A) $45 ^ { \circ }$
B) $4 ^ { \circ }$
C) $1 ^ { \circ }$
D) $45 \pi ^ { \circ }$

Question 56

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?

A) $17.79 \mathrm { in } ^ { 2 }$
B) $35.59 \mathrm { in } ^ { 2 }$
C) $302.49 \mathrm { in } ^ { 2 }$
D) $604.97 \mathrm { in } ^ { 2 }$

Question 57

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $\mathrm { r } = 22.1$ feet, $\theta = 11.19 ^ { \circ } , \mathrm { A } =$ ?

A) $50.69 \mathrm { ft } ^ { 2 }$
B) $98.38 \mathrm { ft } ^ { 2 }$
C) $95.38 \mathrm { ft } ^ { 2 }$
D) $47.69 \mathrm { ft } ^ { 2 }$

Question 58

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $$\theta = 60 ^ { \circ } , \mathrm { A } = 100 \text { square meters, } \mathrm { r } = \text { ? }$$

A) $6.26 \mathrm {~m}$
B) $39.25 \mathrm {~m}$
C) $157 \mathrm {~m}$
D) $13.82 \mathrm {~m}$

Question 59

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.

- $$\theta = \frac { \pi } { 4 } \text { radians, } \mathrm { A } = 50 \text { square meters, } \mathrm { r } = \text { ? }$$

A) 11.29 m
B) 4.43 m
C) 19.63 m
D) 78.5 m

Question 60

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places.
5

A) -0.08°
B) 286.48°
C) 286.23°
D) 0.09°

Question 61

Solve the problem.
The Earth rotates about its pole once every 24 hours. The distance from the pole to a location on Earth 35° north latitude is about 3,243.8 miles. Therefore, a location on Earth at 35° north latitude is spinning on a circle of
Radius 3,243.8 miles. Compute the linear speed on the surface of the Earth at 35° north latitude.

A) 135 mph
B) 20,381 mph
C) 795 mph
D) 849 mph

Question 62

Solve the problem.

-In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of $$2.4 \times 10 ^ { 4 }$$ miles. The orbit is circular, and one revolution around Earth takes 10.1 days. Assuming the radius of the Earth is 3960
Miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile.

A) 115 mph
B) 725 mph
C) 15,322 mph
D) 622 mph

Question 63

Solve the problem.
A weight hangs from a rope 20 feet long. It swings through an angle of 27° each second. How far does the weight travel each second? Round to the nearest 0.1 foot.

A) 9.0 feet
B) 8.7 feet
C) 9.4 feet
D) 8.1 feet

Question 64

Solve the problem.

-An irrigation sprinkler in a field of lettuce sprays water over a distance of 35 feet as it rotates through an angle of 135°. What area of the field receives water? If necessary, round the answer to two decimal places.

A) $459.38 \mathrm { ft } ^ { 2 }$
B) $2,886.34 \mathrm { ft } ^ { 2 }$
C) $1,443.17 \mathrm { ft } ^ { 2 }$
D) $41.23 \mathrm { ft } ^ { 2 }$

Question 65

Solve the problem.

-An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?

A) $2 \mathrm {~m} / \mathrm { sec }$
B) $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$
C) $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$
D) $3 \mathrm {~m} / \mathrm { sec }$

Question 66

Solve the problem.

-An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of $\frac { 1 } { 5 }$ radian is swept out, what is the linear speed of the object?

A) $\frac { 1 } { 4 } \mathrm {~m} / \mathrm { sec }$
B) $\frac { 1 } { 8 } \mathrm {~m} / \mathrm { sec }$
C) $\frac { 2 } { 5 } \mathrm {~m} / \mathrm { sec }$
D) $\frac { 1 } { 5 } \mathrm {~m} / \mathrm { sec }$

Question 67

Solve the problem.
A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour
Rounded to the nearest whole number.

A) 9 mph
B) 47 mph
C) 28 mph
D) 56 mph

Question 68

Find the area A. Round the answer to three decimal places.

-

A) $31.416 \mathrm{ft}^{2}$
B) $62.832 \mathrm{ft} 2$
C) $20 \mathrm{ft}^{2}$
D) $3.142 \mathrm{ft}^{2}$

Question 69

Solve the problem.
A car is traveling at 50 mph. If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.

A) 638.41 rpm
B) 1,292.82 rpm
C) 4,061.54 rpm
D) 646.41 rpm

Question 70

Solve the problem.

-A gear with a radius of 16 centimeters is turning at $\frac { \pi } { 11 }$ radians/sec. What is the linear speed at a point on the outer edge of the gear?

A) $\frac { 11 \pi } { 16 } \mathrm {~cm} / \mathrm { sec }$
B) $\frac { \pi } { 176 } \mathrm {~cm} / \mathrm { sec }$
C) $176 \pi \mathrm { cm } / \mathrm { sec }$
D) $\frac { 16 \pi } { 11 } \mathrm {~cm} / \mathrm { sec }$

Question 71

Solve the problem.
A wheel of radius 3.4 feet is moving forward at 18 feet per second. How fast is the wheel rotating?

A) 0.19 radians/sec
B) 5.7 radians/sec
C) 5.3 radians/sec
D) 0.92 radians/sec

Question 72

Find the area A. Round the answer to three decimal places.

-

A) $6.944 \mathrm { yd } ^ { 2 }$
B) $2.182 \mathrm { yd } ^ { 2 }$
C) $21.817 \mathrm { yd } ^ { 2 }$
D) $43.633 \mathrm { yd } ^ { 2 }$

Question 73

Solve the problem.

-A circle has a radius of 8 centimeters. Find the area of the sector of the circle formed by an angle of 60°. If necessary, round the answer to two decimal places.

A) $33.51 \mathrm {~cm} ^ { 2 }$
B) $67.02 \mathrm {~cm} ^ { 2 }$
C) $2.22 \mathrm {~cm} ^ { 2 }$
D) $4.19 \mathrm {~cm} ^ { 2 }$

Question 74

Find the area A. Round the answer to three decimal places.

-

A) $0.778 \mathrm{~cm}^{2}$
B) $1.222 \mathrm{~cm}^{2}$
C) $4.887 \mathrm{~cm}^{2}$
D) $2.443\mathrm{~cm}^{2}$

Question 75

Solve the problem.

-An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of $$\frac { 1 } { 3 }$$ radian is swept out, what is the linear speed of the object?

A) $\frac { 1 } { 6 }$ radians/sec
B) $6 \mathrm {~cm} / \mathrm { sec }$
C) 6 radians/sec
D) $\frac { 1 } { 6 } \mathrm {~cm} / \mathrm { sec }$

Question 76

Solve the problem.
To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 11 revolutions per minute, what is the speed of the current? If
Necessary, round to two decimal places.

A) 0.06 mph
B) 34.56 mph
C) 0.2 mph
D) 0.39 mph

Question 77

Solve the problem.
As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 120 square yards in the shape of a sector of a circle of radius 30 yards. Through what angle should the sprinkler be
Set to rotate? If necessary, round the answer to two decimal places.

A) 48°
B) 7.64°
C) 15.28°
D) 11.46°

Question 78

Solve the problem.
A carousel has a radius of 15 feet and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places.

A) 94.25 ft/sec
B) 0.54 ft/sec
C) 3.37 ft/sec
D) 11.73 ft/sec

Question 79

Solve the problem.
The four Galilean moons of Jupiter have orbital periods and mean distances from Jupiter given by the following table. Find the linear speed of each moon. Which is the fastest (in terms of linear speed)?

Question 80

Solve the problem.

-The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle?
(Round to the nearest 0.1 square inch.)

A) $1041.8$ in $^ { 2 }$
B) $1105.3 \mathrm { in } ^ { 2 }$
C) $948.3 \mathrm { in } ^ { 2 }$
D) $1036.7$ in $^ { 2 }$