Question 1

Solve the problem.
-Find $\omega$ for the minute hand of a clock.

Accepted Answer

A)  $\frac { \pi } { 60 }$ radians per min 
B)  $\frac { \pi } { 6 }$ radians per min 
C)  $\frac { \pi } { 30 }$ radians per min 
D)  $30 \pi$ radians per min 
A)  $\frac { \pi } { 60 }$ radians per min 
B)  $\frac { \pi } { 6 }$ radians per min 
C)  $\frac { \pi } { 30 }$ radians per min 
D)  $30 \pi$ radians per min

Question 2

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place.
-$\mathrm { r } = 16.05 \mathrm {~cm}$.; $\theta = \frac { 4 } { 3 } \pi$ radians

Accepted Answer

A)  $33.6 \mathrm {~cm}$ 
B)  $134.5 \mathrm {~cm}$ 
C)  $67.2 \mathrm {~cm}$ 
D)  $21.4 \mathrm {~cm}$ 
A)  $33.6 \mathrm {~cm}$ 
B)  $134.5 \mathrm {~cm}$ 
C)  $67.2 \mathrm {~cm}$ 
D)  $21.4 \mathrm {~cm}$

Question 3

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$14 \pi$

Accepted Answer

A)  $1260 ^ { \circ }$ 
B)  $2700 ^ { \circ }$ 
C)  $5040 ^ { \circ }$ 
D)  $2520 ^ { \circ }$ 
A)  $1260 ^ { \circ }$ 
B)  $2700 ^ { \circ }$ 
C)  $5040 ^ { \circ }$ 
D)  $2520 ^ { \circ }$

Question 4

$$\text { Find the value of } s \text { in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$$
-cos s = 0.6784

Accepted Answer

A) 0.8252 
B) 0.7456 
C) 5.4580 
D) 0.9668 
A) 0.8252 
B) 0.7456 
C) 5.4580 
D) 0.9668

Question 5

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.

Accepted Answer

A)  $0.5878$ 
B)  $1.3764$ 
C)  $0.8090$ 
D)  $0.7265$ 
A)  $0.5878$ 
B)  $1.3764$ 
C)  $0.8090$ 
D)  $0.7265$

Question 6

$$\text { Use the formula } \omega = \frac { \theta } { t } \text { to find the value of the missing variable. Give an exact answer unless otherwise indicated. }$$
-$\omega = \frac { \pi } { 8 }$ radian per min, $\mathrm { t } = 11 \mathrm {~min}$

Accepted Answer

A)  $\frac { 11 \pi } { 8 }$ radians 
B)  $\frac { 88 } { \pi }$ radians 
C)  $\frac { \pi } { 88 }$ radian 
D)  $\frac { 8 \pi } { 11 }$ radians 
A)  $\frac { 11 \pi } { 8 }$ radians 
B)  $\frac { 88 } { \pi }$ radians 
C)  $\frac { \pi } { 88 }$ radian 
D)  $\frac { 8 \pi } { 11 }$ radians

Question 7

Find the exact values of s in the given interval that satisfy the given condition.
-$$[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$$

Accepted Answer

A)  $- \frac { 5 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 }$ 
B)  $- \frac { 5 \pi } { 3 } , - \frac { 4 \pi } { 3 } , - \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
C)  $- \frac { 11 \pi } { 6 } , - \frac { 7 \pi } { 6 } , - \frac { 5 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $- \frac { 11 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 }$ 
A)  $- \frac { 5 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 }$ 
B)  $- \frac { 5 \pi } { 3 } , - \frac { 4 \pi } { 3 } , - \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
C)  $- \frac { 11 \pi } { 6 } , - \frac { 7 \pi } { 6 } , - \frac { 5 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $- \frac { 11 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 }$

Question 8

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

Accepted Answer

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

Question 9

Solve the problem.
-A sensor light installed on the edge of a home can detect motion for a distance of $69 \mathrm { ft }$. in front and with a range of motion of $262 ^ { \circ }$. Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

Accepted Answer

A)  $10,885.36 \mathrm { ft } ^ { 2 }$ 
B)  $10,885.46 \mathrm { ft } ^ { 2 }$ 
C)  $21,771.02 \mathrm { ft } ^ { 2 }$ 
D)  $21,770.92 \mathrm { ft } ^ { 2 }$ 
A)  $10,885.36 \mathrm { ft } ^ { 2 }$ 
B)  $10,885.46 \mathrm { ft } ^ { 2 }$ 
C)  $21,771.02 \mathrm { ft } ^ { 2 }$ 
D)  $21,770.92 \mathrm { ft } ^ { 2 }$

Question 10

$$\text { Find the value of } \mathrm { s } \text { in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$$
-csc s = 1.1691

Accepted Answer

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

Question 11

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.

Accepted Answer

A)  $0.9325$ 
B)  $0.7314$ 
C)  $0.6820$ 
D)  $1.3673$ 
A)  $0.9325$ 
B)  $0.7314$ 
C)  $0.6820$ 
D)  $1.3673$

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 PQ.

Accepted Answer

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

Question 13

Solve the problem.
-Find the measure (in radians)of a central angle of a sector of area 55 square inches in a circle of radius 8 inches. Round to the nearest hundredth.

Accepted Answer

A) 3.44 radians 
B) 2.58 radians 
C) 0.86 radians 
D) 1.72 radians 
A) 3.44 radians 
B) 2.58 radians 
C) 0.86 radians 
D) 1.72 radians

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.

Accepted Answer

A)  $10 \pi \mathrm { in }$. 
B)  $5 \pi \mathrm { in }$. 
C)  $2.5 \pi \mathrm { in }$. 
D)  $25 \pi \mathrm { in }$. 
A)  $10 \pi \mathrm { in }$. 
B)  $5 \pi \mathrm { in }$. 
C)  $2.5 \pi \mathrm { in }$. 
D)  $25 \pi \mathrm { in }$.

Question 15

Find the exact value without using a calculator.
-$$\tan \frac { - 5 \pi } { 6 }$$

Accepted Answer

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

Question 16

$$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$$
-83.88°

Accepted Answer

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

Question 17

Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$$

Accepted Answer

A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { \pi } { 3 }$ 
C)  $s = \frac { 11 \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 3 }$ 
A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { \pi } { 3 }$ 
C)  $s = \frac { 11 \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 3 }$

Question 18

Convert the degree measure to radians, correct to four decimal places. Use $$\text { Use } 3.1416 \text { for } \pi \text {. }$$
-31°

Accepted Answer

A) 0.3607 
B) 1.0821 
C) 0.5411 
D) 0.2705 
A) 0.3607 
B) 1.0821 
C) 0.5411 
D) 0.2705

Question 19

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. $$\text { Use } 3.1416 \text { for }$$
--3.4

Accepted Answer

A) -389.32° 
B) -389.62° 
C) -194.81° 
D) -195.11° 
A) -389.32° 
B) -389.62° 
C) -194.81° 
D) -195.11°

Question 20

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

Accepted Answer

The answer of Find the specified quantity.
-Find the value of...

Solve the problem. -Find $\omega$ for the minute hand of a clock.

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 16.05 \mathrm {~cm}$ .; $\theta = \frac { 4 } { 3 } \pi$ radians

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $14 \pi$

$\text { Find the value of } s \text { in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -cos s = 0.6784

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.

$\text { Use the formula } \omega = \frac { \theta } { t } \text { to find the value of the missing variable. Give an exact answer unless otherwise indicated. }$ - $\omega = \frac { \pi } { 8 }$ radian per min, $\mathrm { t } = 11 \mathrm {~min}$

Find the exact values of s in the given interval that satisfy the given condition. - $[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$

Solve the problem. -A sensor light installed on the edge of a home can detect motion for a distance of $69 \mathrm { ft }$ . in front and with a range of motion of $262 ^ { \circ }$ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

$\text { Find the value of } \mathrm { s } \text { in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -csc s = 1.1691

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.

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

Solve the problem. -Find the measure (in radians)of a central angle of a sector of area 55 square inches in a circle of radius 8 inches. Round to the nearest hundredth.

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.

Find the exact value without using a calculator. - $\tan \frac { - 5 \pi } { 6 }$

$\text { Convert the degree measure to radians, correct to four decimal places. Use } 3.1416 \text { for } \pi \text {. }$ -83.88°

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \cos s = \frac { 1 } { 2 }$

Convert the degree measure to radians, correct to four decimal places. Use $\text { Use } 3.1416 \text { for } \pi \text {. }$ -31°

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. $\text { Use } 3.1416 \text { for }$ --3.4

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

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

Solve the problem. -Find ω\omegaω for the minute hand of a clock.

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. - r=16.05 cm\mathrm { r } = 16.05 \mathrm {~cm}r=16.05 cm .; θ=43π\theta = \frac { 4 } { 3 } \piθ=34​π radians

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 14π14 \pi14π