Deck 3: Radian Measure and the Unit Circle

Question 1

Use a table or a calculator to evaluate the function. Round to four decimal places.
sec 0.2020

A)0.9797
B)1.0208
C)0.2048
D)0.2006

Answer 1

B

Question 2

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.

Answer 2

B

Question 3

Find the specified quantity.

Answer 3

Question 4

Solve the problem.

Question 5

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 6

83.88°

A)1.5640
B)1.4640
C)1.3640
D)1.2640

Question 7

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-160°41´

A)-2.8045
B)-2.7945
C)-2.7745
D)-2.7845

Question 8

0.8996

A)52.04°
B)52.54°
C)51.54°
D)50.84°

Question 9

4
Provide an appropriate response.

Question 10

Solve the problem.

Question 11

Find the specified quantity.
If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central
angle changed?

Question 12

Find the specified quantity.

Question 13

Solve the problem.

Question 14

Solve the problem.
Suppose the tip of the minute hand of a clock is 15 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 10 minutes. Give an exact answer.

Question 15

Find the exact value of s in the given interval that has the given circular function value.

Question 16

Find the exact value without using a calculator.

Question 17

Find the specified quantity.
Find the value of the arc length when ϴ (the central Angle)is given in degrees instead of
radians.

Question 18

Find the exact circular function value.

Question 19

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 20

For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.
s = 47

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

Question 21

351°10´

A)6.109
B)6.099
C)6.129
D)6.119

Question 22

cot s = 0.6921

A)0.3178
B)0.9654
C)0.7470
D)4.1070

Question 23

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 24

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 25

Find the exact circular function value.

Question 26

Solve the problem.

Question 27

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
72°

A)1.0566
B)1.1566
C)0.9566
D)1.2566

Question 28

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
sin s = 0.5954

A)-0.4962
B)0.6378
C)0.6454
D)2.5038

Question 29

Solve the problem.
The minute hand of a clock is 13 inches long. What distance does its tip move in 16 minutes? Give an exact answer.

Question 30

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 43.15° N, are 486 km apart.

A)38.8 °N
B)39.5 °N
C)47.5 °N
D)52.46 °N

Question 31

tan s = 7.6725

A)1.4412
B)0.8420
C)1.0120
D)4.5828

Question 32

Find the exact circular function value.

Question 33

Solve the problem.
A circular pulley is rotating about its center. Through how many radians would it turn in 22 r otations?

Question 34

Find the exact value without using a calculator.

Question 35

Find the exact values of s in the given interval that satisfy the given condition.

Question 36

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 37

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.

Question 38

Solve the problem.
Suppose the tip of the minute hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Question 39

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.

Question 40

Solve the problem.
Electrical wire is being wound around a drum with radius of 1.49 meters. How much line (to the nearest hundredth of a meter)would be wound around the drum if it is rotated through an angle of
275.3°?

A)7.16 m
B)7.26 m
C)6.96 m
D)7.06 m

Question 41

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
Find csc ϴ.

Question 42

Solve the problem.

Question 43

Find the corresponding angle measure in radians.
-150°

Question 44

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.

Question 45

Solve the problem.

Question 46

Solve the problem.
Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 43°, find the length of OQ accurate to four decimal places.

Question 47

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated.
v = 218.9 m per sec, Ɯ = 0.63361 radian per sec (Round to four decimal places when necessary.)

A)69.6779 m
B)4.9583 m
C)345.4807 m
D)0.0029 m

Question 48

Find the exact value of s in the given interval that has the given circular function value.

Question 49

Convert the degree measure to radians, correct to four decimal places. Use
81.4687°

A)1.7219
B)1.5219
C)1.6219
D)1.4219

Question 50

Use a table or a calculator to evaluate the function. Round to four decimal places.
csc 0.2475

A)0.9695
B)0.2450
C)1.0314
D)4.0820

Question 51

Find the exact circular function value.

Question 52

s = 5.6

A)(-0.7756, °°°)
B)(-0.6313, 0.7756)
C)(0.7756, -0.6313)
D)(-0.7756, -0.6313)

Question 53

sec s = 3.7404

A)0.2706
B)1.8414
C)1.3002
D)4.9830

Question 54

Use a table or a calculator to evaluate the function. Round to four decimal places.
cot 0.2258

A)0.9746
B)0.2297
C)1.0260
D)4.3532

Question 55

Convert the degree measure to radians. Leave answer as a multiple of π.
1800°

Question 56

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .

Question 57

Solve the problem.

Question 58

Approximate the length using the formula for arc length. Round to the nearest meter.
A tree 460 m away subtends an angle of 2°. Find the height of the tree.

A)32 m
B)13 m
C)16 m
D)35 m

Question 59

Convert the degree measure to radians. Leave answer as a multiple of
-45°

Question 60

Solve the problem.
Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 54°, find the length of VR accurate to four decimal places.

Question 61

Find the exact value of s in the given interval that has the given circular function value.

Question 62

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.

Question 63

For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.
s = 66

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

Question 64

Solve the problem.
A pulley of radius 25 cm rotates 7 times in 4 sec. Find the angular speed of the pulley.

Question 65

Solve the problem.
Find the radius (to the nearest hundredth of a millimeter)of a pulley if rotating the pulley 109.38° raises the pulley 42.2 mm.

A)22.01 mm
B)22.21 mm
C)22.11 mm
D)21.91 mm

Question 66

s = -6.2

A)(-0.9965, -0.0831)
B)(0.9965, -0.0831)
C)(0.9965, 0.0831)
D)(°°°, 0.9965)

Question 67

Solve the problem.
Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 13°, find the length of US accurate to four decimal places.

Question 68

Find the exact value without using a calculator.

Question 69

Solve the problem.
Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 45°, find the exact length of VR.

Question 70

Solve the problem.

Question 71

Use the formula s = rωt to find the value of the missing variable. Give an exact answer.

Question 72

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.

Question 73

Find the exact value without using a calculator.

Question 74

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.

Question 75

Solve the problem.
A wheel with a 36-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 12 inches. What is the angle (to the nearest tenth of a degree)
Between the radii to the two marks?

A)17.1°
B)19.1°
C)21.1°
D)15.1°

Question 76

Solve the problem.
What is the difference in area covered by a single 12-inch windshield wiper operating with a central angle of 126° compared to a pair of 2-inch wipers operating together each having a central
Angle of 108°? Round to the nearest hundredth.

Question 77

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
Find cot ϴ.

Question 78

csc s = 1.1691

A)0.8262
B)1.0262
C)0.9262
D)1.1262

Question 79

Solve the problem.

Question 80

Find the exact value without using a calculator.