Question 1

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

Accepted Answer

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

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.
-$$\mathrm { r } = 7.4 \mathrm { mi } , \theta = 314 ^ { \circ }$$

Accepted Answer

A)  $55.6 \mathrm { mi } ^ { 2 }$ 
B)  $20.3 \mathrm { mi } ^ { 2 }$ 
C)  $300.1 \mathrm { mi } ^ { 2 }$ 
D)  $150.1 \mathrm { mi } ^ { 2 }$ 
A)  $55.6 \mathrm { mi } ^ { 2 }$ 
B)  $20.3 \mathrm { mi } ^ { 2 }$ 
C)  $300.1 \mathrm { mi } ^ { 2 }$ 
D)  $150.1 \mathrm { mi } ^ { 2 }$

Question 3

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per sec

Accepted Answer

A)  $\frac { 3 \pi } { 16 } \mathrm {~cm}$ per sec 
B)  $\frac { 16 \pi } { 3 } \mathrm {~cm}$ per sec 
C)  $48 \pi \mathrm { cm }$ per sec 
D)  $\frac { \pi } { 48 } \mathrm {~cm}$ per sec 
A)  $\frac { 3 \pi } { 16 } \mathrm {~cm}$ per sec 
B)  $\frac { 16 \pi } { 3 } \mathrm {~cm}$ per sec 
C)  $48 \pi \mathrm { cm }$ per sec 
D)  $\frac { \pi } { 48 } \mathrm {~cm}$ per sec

Question 4

Find the exact circular function value.
-$$\sec \frac { 3 \pi } { 4 }$$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $- 2$ 
D)  $- \sqrt { 2 }$ 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $- 2$ 
D)  $- \sqrt { 2 }$

Question 5

Convert the degree measure to radians, correct to four decimal places. Use $$\text { Use } 3.1416 \text { for } \pi \text {. }$$
-39.3222°

Accepted Answer

A) 0.6863 
B) 0.8863 
C) 0.5863 
D) 0.7863 
A) 0.6863 
B) 0.8863 
C) 0.5863 
D) 0.7863

Question 6

Convert the degree measure to radians. Leave answer as a multiple of π.
-270°

Accepted Answer

A)  $3 \pi$ 
B)  $- \frac { 3 \pi } { 4 }$ 
C)  $- \frac { 3 \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$ 
A)  $3 \pi$ 
B)  $- \frac { 3 \pi } { 4 }$ 
C)  $- \frac { 3 \pi } { 2 }$ 
D)  $\frac { 3 \pi } { 2 }$

Question 7

Find the specified quantity.
-$$\text { Is it correct to say that the value of } \cos 45 = \frac { \sqrt { 2 } } { 2 } \text { ? Explain your answer. }$$

Accepted Answer

No, it is not correct because

Question 8

Find the exact circular function value.
-$\csc \frac { - 2 \pi } { 3 }$

Accepted Answer

A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $- \sqrt { 3 }$ 
A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $- \sqrt { 3 }$

Question 9

Convert the degree measure to radians. Leave answer as a multiple of π.
-288°

Accepted Answer

A)  $\frac { 16 \pi } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 5 }$ 
D)  $\frac { 4 \pi } { 5 }$ 
A)  $\frac { 16 \pi } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 5 }$ 
D)  $\frac { 4 \pi } { 5 }$

Question 10

Use the formula s = rωt to find the value of the missing variable. Give an exact answer.
-$\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 5 }$ radian per sec, $\mathrm { t } = 16 \mathrm { sec }$

Accepted Answer

A)  $\frac { 32 \pi } { 5 } \mathrm {~cm}$ 
B)  $\frac { 5 \pi } { 32 } \mathrm {~cm}$ 
C)  $\frac { 5 } { 32 \pi } \mathrm { cm }$ 
D)  $\frac { 32 } { 5 \pi } \mathrm { cm }$ 
A)  $\frac { 32 \pi } { 5 } \mathrm {~cm}$ 
B)  $\frac { 5 \pi } { 32 } \mathrm {~cm}$ 
C)  $\frac { 5 } { 32 \pi } \mathrm { cm }$ 
D)  $\frac { 32 } { 5 \pi } \mathrm { cm }$

Question 11

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.
-$\mathrm { r } = 7.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

Accepted Answer

A)  $15.4 \mathrm { ft } ^ { 2 }$ 
B)  $7.3 \mathrm { ft } ^ { 2 }$ 
C)  $102.6 \mathrm { ft } ^ { 2 }$ 
D)  $51.3 \mathrm { ft } ^ { 2 }$ 
A)  $15.4 \mathrm { ft } ^ { 2 }$ 
B)  $7.3 \mathrm { ft } ^ { 2 }$ 
C)  $102.6 \mathrm { ft } ^ { 2 }$ 
D)  $51.3 \mathrm { ft } ^ { 2 }$

Question 12

Solve the problem.
-A wheel with a 21-inch diameter is turning at the rate of 44 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Accepted Answer

A) 2903 in./min 
B) 2956 in./min 
C) 2949 in./min 
D) 2910 in./min 
A) 2903 in./min 
B) 2956 in./min 
C) 2949 in./min 
D) 2910 in./min

Question 13

Find the exact circular function value.
-$$\sin \frac { 4 \pi } { 3 }$$

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  -1 
D)  $- \frac { 1 } { 2 }$ 
A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  -1 
D)  $- \frac { 1 } { 2 }$

Question 14

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
-Find $\sin \theta$.

Accepted Answer

A)  $- \frac { 7 } { 24 }$ 
B)  $\frac { 24 } { 25 }$ 
C)  $- \frac { 24 } { 25 }$ 
D)  $\frac { 7 } { 25 }$ 
A)  $- \frac { 7 } { 24 }$ 
B)  $\frac { 24 } { 25 }$ 
C)  $- \frac { 24 } { 25 }$ 
D)  $\frac { 7 } { 25 }$

Question 15

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

Accepted Answer

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

Question 16

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?

Accepted Answer

A) 17.1° 
B) 19.1° 
C) 21.1° 
D) 15.1° 
A) 17.1° 
B) 19.1° 
C) 21.1° 
D) 15.1°

Question 17

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

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  0 
C)  1 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
A)  $\sqrt { 2 }$ 
B)  0 
C)  1 
D)  $\frac { \sqrt { 2 } } { 2 }$

Question 18

Solve the problem.
-A pendulum swinging through a central angle of 67° completes an arc of length 7.2 cm. What is the length of the pendulum? Round to the nearest hundredth.

Accepted Answer

A) 6.16 cm 
B) 5.96 cm 
C) 6.26 cm 
D) 6.06 cm 
A) 6.16 cm 
B) 5.96 cm 
C) 6.26 cm 
D) 6.06 cm

Question 19

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

Accepted Answer

A)  $66 \pi$ 
B)  $110 \pi$ 
C)  $88 \pi$ 
D)  $44 \pi$ otations? 
A)  $66 \pi$ 
B)  $110 \pi$ 
C)  $88 \pi$ 
D)  $44 \pi$ otations?

Question 20

Solve the problem.
-Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 8.8 centimeters and the radius of the larger wheel
Is 16.9 centimeters. Through how many degrees (to the nearest hundredth of a degree)will the
Larger wheel rotate if the smaller one rotates 180°?

Accepted Answer

A) 94.73° 
B) 93.73° 
C) 95.73° 
D) 93.63° 
A) 94.73° 
B) 93.73° 
C) 95.73° 
D) 93.63°

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

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 7.4 \mathrm { mi } , \theta = 314 ^ { \circ }$

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per sec

Find the exact circular function value. - $\sec \frac { 3 \pi } { 4 }$

Convert the degree measure to radians, correct to four decimal places. Use $\text { Use } 3.1416 \text { for } \pi \text {. }$ -39.3222°

Convert the degree measure to radians. Leave answer as a multiple of π. -270°

Find the specified quantity. - $\text { Is it correct to say that the value of } \cos 45 = \frac { \sqrt { 2 } } { 2 } \text { ? Explain your answer. }$

Find the exact circular function value. - $\csc \frac { - 2 \pi } { 3 }$

Convert the degree measure to radians. Leave answer as a multiple of π. -288°

Use the formula s = rωt to find the value of the missing variable. Give an exact answer. - $\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 5 }$ radian per sec, $\mathrm { t } = 16 \mathrm { sec }$

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 7.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

Solve the problem. -A wheel with a 21-inch diameter is turning at the rate of 44 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Find the exact circular function value. - $\sin \frac { 4 \pi } { 3 }$

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

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?

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

Solve the problem. -A pendulum swinging through a central angle of 67° completes an arc of length 7.2 cm. What is the length of the pendulum? Round to the nearest hundredth.

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

Trigonometric Functions

Acute Angles and Right Triangles

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 3: Radian Measure and the Unit Circle