Question 1

$$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$$
-tan s = 7.6725

Accepted Answer

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

Question 2

Find the exact value without using a calculator.
-$$\csc \frac { 5 \pi } { 3 }$$

Accepted Answer

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

Question 3

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.
-$\mathrm { r } = 44.6 \mathrm {~cm} , \theta = \frac { \pi } { 13 }$ radians

Accepted Answer

A)  $5.4 \mathrm {~cm} ^ { 2 }$ 
B)  $240.4 \mathrm {~cm} ^ { 2 }$ 
C)  $76.5 \mathrm {~cm} ^ { 2 }$ 
D)  $480.8 \mathrm {~cm} ^ { 2 }$ 
A)  $5.4 \mathrm {~cm} ^ { 2 }$ 
B)  $240.4 \mathrm {~cm} ^ { 2 }$ 
C)  $76.5 \mathrm {~cm} ^ { 2 }$ 
D)  $480.8 \mathrm {~cm} ^ { 2 }$

Question 4

Solve the problem.
-A circular sector has an area of $486 \mathrm { ft } ^ { 2 }$. The radius of the circle is 9 feet. What is the arc length of the sector?

Accepted Answer

A)  $110 \mathrm { ft }$ 
B)  $12 \mathrm { ft }$ 
C)  $108 \mathrm { ft }$ 
D)  $54 \mathrm { ft }$ 
A)  $110 \mathrm { ft }$ 
B)  $12 \mathrm { ft }$ 
C)  $108 \mathrm { ft }$ 
D)  $54 \mathrm { ft }$

Question 5

Suppose an arc of length $s$ lies on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$, starting at point $( 1,0 )$ and terminating at the point ( $\left. x , y \right)$. Use a calculator to find the approximate coordinates ( $x , y )$. Round coordinates to four decimal places when appropriate.

The unit circle $x ^ { 2 } + y ^ { 2 } = 1$
-s = -6.2

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find the corresponding angle measure in radians.
-45°

Accepted Answer

A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 4 \pi } { 7 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { 3 \pi } { 4 }$ 
A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 4 \pi } { 7 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { 3 \pi } { 4 }$

Question 8

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-v = 12 ft per sec, r = 1.6 ft (Round to four decimal places when necessary.)

Accepted Answer

A) 3.8197 radians per sec 
B) 7.5 radians per sec 
C) 1.9635 radian per sec 
D) 0.1333 radian per sec 
A) 3.8197 radians per sec 
B) 7.5 radians per sec 
C) 1.9635 radian per sec 
D) 0.1333 radian per sec

Question 9

Solve the problem.
-An object is spinning around a circle with a radius of 20 centimeters. If in 17 seconds a central angle of $\frac { 1 } { 18 }$ radian has been covered, what is the linear speed of the object?

Accepted Answer

A)  $\frac { 170 } { 9 } \mathrm {~cm}$ per sec 
B)  $\frac { 20 } { 153 } \mathrm {~cm}$ per sec 
C)  $20 \mathrm {~cm}$ per $\mathrm { sec }$ 
D)  $\frac { 10 } { 153 } \mathrm {~cm}$ per sec 
A)  $\frac { 170 } { 9 } \mathrm {~cm}$ per sec 
B)  $\frac { 20 } { 153 } \mathrm {~cm}$ per sec 
C)  $20 \mathrm {~cm}$ per $\mathrm { sec }$ 
D)  $\frac { 10 } { 153 } \mathrm {~cm}$ per sec

Question 10

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

Accepted Answer

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

Question 11

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)  $- \frac { 12 } { 13 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $- \frac { 5 } { 13 }$ 
A)  $- \frac { 12 } { 13 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $- \frac { 5 } { 13 }$

Question 12

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

Accepted Answer

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

Question 13

Find the exact values of s in the given interval that satisfy the given condition.
-$$[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$$

Accepted Answer

A)  $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $- \frac { 7 \pi } { 4 } , - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 }$ 
C)  $- \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
D)  $- \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 }$ 
A)  $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $- \frac { 7 \pi } { 4 } , - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 }$ 
C)  $- \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
D)  $- \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 }$

Question 14

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$$- \frac { 9 \pi } { 6 }$$

Accepted Answer

A)  $- 269.5 ^ { \circ }$ 
B)  $- 270.5 ^ { \circ }$ 
C)  $- 271 ^ { \circ }$ 
D)  $- 270 ^ { \circ }$ 
A)  $- 269.5 ^ { \circ }$ 
B)  $- 270.5 ^ { \circ }$ 
C)  $- 271 ^ { \circ }$ 
D)  $- 270 ^ { \circ }$

Question 15

Convert the degree measure to radians, correct to four decimal places. Use $$\text { Use } 3.1416 \text { for } \pi \text {. }$$
-19°10´

Accepted Answer

A) 0.2345 
B) 0.6345 
C) 0.3345 
D) 0.5345 
A) 0.2345 
B) 0.6345 
C) 0.3345 
D) 0.5345

Question 16

$$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$$
-351°10´

Accepted Answer

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

Question 17

$$\text { Use the formula } \omega = \frac { \theta } { t } \text { to find the value of the missing variable. Give an exact answer unless otherwise indicated. }$$
-$$\theta = \frac { \pi } { 6 } \text { radian, } t = 11 \mathrm { sec }$$

Accepted Answer

A)  $\frac { \pi } { 66 }$ radian per sec 
B)  $\frac { 11 \pi } { 6 }$ radians per sec 
C)  $\frac { 6 \pi } { 11 }$ radians per sec 
D)  $\frac { 66 } { \pi }$ radians per $s e c$ 
A)  $\frac { \pi } { 66 }$ radian per sec 
B)  $\frac { 11 \pi } { 6 }$ radians per sec 
C)  $\frac { 6 \pi } { 11 }$ radians per sec 
D)  $\frac { 66 } { \pi }$ radians per $s e c$

Question 18

Solve the problem.
-A pendulum of length 12.1 inches swings 5°37´ to each side of its vertical position. What is the length (to the nearest hundredth of an inch)of the arc through which the end of the pendulum
Swings?

Accepted Answer

A) 2.07 in. 
B) 2.27 in. 
C) 2.17 in. 
D) 2.37 in. 
A) 2.07 in. 
B) 2.27 in. 
C) 2.17 in. 
D) 2.37 in.

Question 19

Use a table or a calculator to evaluate the function. Round to four decimal places.
-cos 0.1209

Accepted Answer

A) 0.1206 
B) 1.0074 
C) 0.1215 
D) 0.9927 
A) 0.1206 
B) 1.0074 
C) 0.1215 
D) 0.9927

Question 20

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

Accepted Answer

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

$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -tan s = 7.6725

Find the exact value without using a calculator. - $\csc \frac { 5 \pi } { 3 }$

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 44.6 \mathrm {~cm} , \theta = \frac { \pi } { 13 }$ radians

Solve the problem. -A circular sector has an area of $486 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 9 feet. What is the arc length of the sector?

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

Find the corresponding angle measure in radians. -45°

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. -v = 12 ft per sec, r = 1.6 ft (Round to four decimal places when necessary.)

Solve the problem. -An object is spinning around a circle with a radius of 20 centimeters. If in 17 seconds a central angle of $\frac { 1 } { 18 }$ radian has been covered, what is the linear speed of the object?

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

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

Find the exact values of s in the given interval that satisfy the given condition. - $[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 9 \pi } { 6 }$

Convert the degree measure to radians, correct to four decimal places. Use $\text { Use } 3.1416 \text { for } \pi \text {. }$ -19°10´

$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$ -351°10´

$\text { Use the formula } \omega = \frac { \theta } { t } \text { to find the value of the missing variable. Give an exact answer unless otherwise indicated. }$ - $\theta = \frac { \pi } { 6 } \text { radian, } t = 11 \mathrm { sec }$

Solve the problem. -A pendulum of length 12.1 inches swings 5°37´ to each side of its vertical position. What is the length (to the nearest hundredth of an inch)of the arc through which the end of the pendulum Swings?

Use a table or a calculator to evaluate the function. Round to four decimal places. -cos 0.1209

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

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

Find the exact value without using a calculator. - csc⁡5π3\csc \frac { 5 \pi } { 3 }csc35π​

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest tenth. - r=44.6 cm,θ=π13\mathrm { r } = 44.6 \mathrm {~cm} , \theta = \frac { \pi } { 13 }r=44.6 cm,θ=13π​ radians

Solve the problem. -A circular sector has an area of 486ft2486 \mathrm { ft } ^ { 2 }486ft2 . The radius of the circle is 9 feet. What is the arc length of the sector?