Question 1

Solve the problem.
-Through how many radians will the hour hand on a clock rotate in 12 hours?

Accepted Answer

A)  $4 \pi$ 
B)  $\pi$ 
C)  $3 \pi$ 
D)  $2 \pi$ 
A)  $4 \pi$ 
B)  $\pi$ 
C)  $3 \pi$ 
D)  $2 \pi$ D

Question 2

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°?

Accepted Answer

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

Question 3

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$$\frac { 4 \pi } { 9 }$$

Accepted Answer

A)  $81 ^ { \circ }$ 
B)  $80 ^ { \circ }$ 
C)  $80.5 ^ { \circ }$ 
D)  $79.5 ^ { \circ }$ 
A)  $81 ^ { \circ }$ 
B)  $80 ^ { \circ }$ 
C)  $80.5 ^ { \circ }$ 
D)  $79.5 ^ { \circ }$ B

Question 4

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

Accepted Answer

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

Question 5

Find the exact value without using a calculator.
-$\cos \left( \frac { 2 \pi } { 3 } \right)$

Accepted Answer

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

Question 6

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

Accepted Answer

A)  $\frac { \pi } { 6 } \circ$ 
B)  $0.523 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $30 \pi ^ { \circ }$ 
A)  $\frac { \pi } { 6 } \circ$ 
B)  $0.523 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $30 \pi ^ { \circ }$

Question 7

Convert the degree measure to radians, correct to four decimal places. Use $$\text { Use } 3.1416 \text { for } \pi \text {. }$$
-81.4687°

Accepted Answer

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

Question 8

Solve the problem.
-Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 32°, find the length of PQ accurate to four decimal places.

Accepted Answer

A)  $1.8871$ 
B)  $0.5299$ 
C)  $0.8480$ 
D)  $0.6249$ 
A)  $1.8871$ 
B)  $0.5299$ 
C)  $0.8480$ 
D)  $0.6249$

Question 9

Provide an appropriate response.
-Describe how an angle measure can be converted from degrees to radians.

Accepted Answer

A)  Multiply the degree measure by $\frac { \pi } { 180 ^ { \circ } }$. 
B)  Multiply the degree measure by $\frac { 90 ^ { \circ } } { \pi }$. 
C)  Multiply the degree measure by $\frac { 180 ^ { \circ } } { \pi }$. 
D)  Multiply the degree measure by $\frac { \pi } { 360 ^ { \circ } }$. 
A)  Multiply the degree measure by $\frac { \pi } { 180 ^ { \circ } }$. 
B)  Multiply the degree measure by $\frac { 90 ^ { \circ } } { \pi }$. 
C)  Multiply the degree measure by $\frac { 180 ^ { \circ } } { \pi }$. 
D)  Multiply the degree measure by $\frac { \pi } { 360 ^ { \circ } }$.

Question 10

Find the corresponding angle measure in radians.
--150°

Accepted Answer

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

Question 11

Approximate the length using the formula for arc length. Round to the nearest meter.
-A television tower 540 m high subtends an angle of 3°50´. How far away is the tower?

Accepted Answer

A) 4860 m 
B) 8071 m 
C) 4900 m 
D) 8111 m 
A) 4860 m 
B) 8071 m 
C) 4900 m 
D) 8111 m

Question 12

Solve the problem.
-Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 31°, find the length of OU accurate to four decimal places.

Accepted Answer

A)  $0.5150$ 
B)  $1.1666$ 
C)  $1.9416$ 
D)  $0.8572$ 
A)  $0.5150$ 
B)  $1.1666$ 
C)  $1.9416$ 
D)  $0.8572$

Question 13

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

Accepted Answer

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

Question 14

Solve the problem.
-The radius of the tires of a car is 18 inches, and they are revolving at the rate of 651 revolutions per minute. How fast is the car traveling in miles per hour?

Accepted Answer

A)  $\frac { 5859 } { 22 } \pi \mathrm { mph }$ 
B)  $\frac { 1953 } { 88 } \pi \mathrm { mph }$ 
C)  $\frac { 1953 } { 880 } \pi \mathrm { mph }$ 
D)  $\frac { 1953 } { 176 } \pi \mathrm { mph }$ 
A)  $\frac { 5859 } { 22 } \pi \mathrm { mph }$ 
B)  $\frac { 1953 } { 88 } \pi \mathrm { mph }$ 
C)  $\frac { 1953 } { 880 } \pi \mathrm { mph }$ 
D)  $\frac { 1953 } { 176 } \pi \mathrm { mph }$

Question 15

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.

Accepted Answer

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

Question 16

Find the exact value without using a calculator.
-$$\sec \frac { 3 \pi } { 4 }$$

Accepted Answer

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

Question 17

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

Accepted Answer

A)  $\mathrm { s } = \frac { 3 \pi } { 4 }$ 
B)  $s = \frac { 5 \pi } { 6 }$ 
C)  $s = \frac { 2 \pi } { 3 }$ 
D)  $s = \frac { \pi } { 4 }$ 
A)  $\mathrm { s } = \frac { 3 \pi } { 4 }$ 
B)  $s = \frac { 5 \pi } { 6 }$ 
C)  $s = \frac { 2 \pi } { 3 }$ 
D)  $s = \frac { \pi } { 4 }$

Question 18

Solve the problem.
-A pulley rotates through 57° in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make in an hour?

Accepted Answer

A) 171.0 rotations 
B) 19.0 rotations 
C) 9.5 rotations 
D) 342.0 rotations 
A) 171.0 rotations 
B) 19.0 rotations 
C) 9.5 rotations 
D) 342.0 rotations

Question 19

$$\text { Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use } 3.1416 \text { for }$$
-0.8996

Accepted Answer

A) 52.04° 
B) 52.54° 
C) 51.54° 
D) 50.84° 
A) 52.04° 
B) 52.54° 
C) 51.54° 
D) 50.84°

Question 20

Convert the degree measure to radians. Leave answer as a multiple of $$\text { of } \pi \text {. }$$
--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)  $\frac { 3 \pi } { 2 }$

Solve the problem. -Through how many radians will the hour hand on a clock rotate in 12 hours?

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°?

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 4 \pi } { 9 }$

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

Find the exact value without using a calculator. - $\cos \left( \frac { 2 \pi } { 3 } \right)$

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

Convert the degree measure to radians, correct to four decimal places. Use $\text { Use } 3.1416 \text { for } \pi \text {. }$ -81.4687°

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 32°, find the length of PQ accurate to four decimal places.

Provide an appropriate response. -Describe how an angle measure can be converted from degrees to radians.

Find the corresponding angle measure in radians. --150°

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower 540 m high subtends an angle of 3°50´. How far away is the tower?

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 31°, find the length of OU accurate to four decimal places.

Solve the problem. -The radius of the tires of a car is 18 inches, and they are revolving at the rate of 651 revolutions per minute. How fast is the car traveling in miles per hour?

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.

Find the exact value without using a calculator. - $\sec \frac { 3 \pi } { 4 }$

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

Solve the problem. -A pulley rotates through 57° in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make in an hour?

$\text { Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use } 3.1416 \text { for }$ -0.8996

Convert the degree measure to radians. Leave answer as a multiple of $\text { of } \pi \text {. }$ --270°

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