Question 1

Evaluate the expression when x is   . Use exact values. 3 cos 6 x

Accepted Answer

The answer of Evaluate the expression when x is ...

Question 2

Find the radian measure of angle θ , if θ  is a central angle in a circle of radius r , and θ  cuts off an arc of length s .    cm,    cm ​

Accepted Answer

A)    
B) 4 
C)    
D)    
E) 5 
A)    
B) 4 
C)    
D)    
E) 5

Question 3

Arc length The minute hand of a clock is 1 centimeter0 long. How far does the tip of the minute hand travel in 35 minutes? Round to three significant digits.
​

Accepted Answer

A) 4.07 centimeters 
B) 3.77 centimeters 
C) 3.47 centimeters 
D) 3.97 centimeters 
E) 3.67 centimeters 
A) 4.07 centimeters 
B) 3.77 centimeters 
C) 3.47 centimeters 
D) 3.97 centimeters 
E) 3.67 centimeters

Question 4

For the problem below, θ  is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 2, r = 5  inches.
​

Accepted Answer

A) s = 10 inches 
B) s = 7 inches 
C) s = 14.3 inches 
D) s = 22.1 inches 
E) s = 6 inches 
A) s = 10 inches 
B) s = 7 inches 
C) s = 14.3 inches 
D) s = 22.1 inches 
E) s = 6 inches

Question 5

Find the area of the sector formed by central angle θ = 2.8 in a circle of radius r = 5 inches. ​

Accepted Answer

A) 35.0 inches 2 
B) 35.4 inches 2 
C) 34.8 inches 2 
D) 34.7 inches 2 
E) 34.9 inches 2 
A) 35.0 inches 2 
B) 35.4 inches 2 
C) 34.8 inches 2 
D) 34.7 inches 2 
E) 34.9 inches 2

Question 6

A light truck with manual transmission has a circular brake drum with a diameter of 323 millimeters. Each brake pad, which presses against the drum, is 308 millimeters long. What central angle is subtended by one of the brake pads? Write your answer in both radians and in degrees. If the answer needs rounding round it to three significant digits.   a = 308  millimeters, b = 323  millimeters 
​__________ radians 
__________ degrees

Accepted Answer

The answer of A light truck with manual transmission has...

Question 7

Find the radian measure of angle θ , if θ  is a central angle in a circle of radius r , and θ  cuts off an arc of length s .    cm,    cm 
θ =  __________ radians

Accepted Answer

The answer of Find the radian measure of angle θ...

Question 8

Use a calculator to find θ to the nearest tenth of a degree, if    and ​   with  θ in QIII ​

Accepted Answer

A) 201.3º 
B) 200.1 º ​ 
C) 196.8 º 
D) 194.8 º 
E) 197.8 º 
A) 201.3º 
B) 200.1 º ​ 
C) 196.8 º 
D) 194.8 º 
E) 197.8 º

Question 9

A lawn sprinkler is located at the corner of a yard. The sprinkler is set to rotate through 90   and project water out 53 feet. What is the area of the yard watered by the sprinkler? If the answer needs rounding, round it to three significant digits. A = __________ feet2

Accepted Answer

Question 10

Point P sweeps out central angle θ  as it rotates on a circle of radius r . Find the angular velocity of point P . Round to the nearest thousandth.   ​

Accepted Answer

A) 0.341 rad/sec 
B) 0.419 rad/sec 
C) 0.402 rad/sec 
D) 0.453 rad/sec 
E) 0.358 rad/sec 
A) 0.341 rad/sec 
B) 0.419 rad/sec 
C) 0.402 rad/sec 
D) 0.453 rad/sec 
E) 0.358 rad/sec

Question 11

Draw the following angle in standard position and then name the reference angle.   ​

Accepted Answer

A) ​   ​     ​ 
B) ​      ​     ​ 
C) ​ ​   ​   
D) ​      ​   
E) ​     ​   
A) ​   ​     ​ 
B) ​      ​     ​ 
C) ​ ​   ​   
D) ​      ​   
E) ​     ​

Question 12

Use the unit circle to find the six trigonometric functions of 240°. ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 13

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 160°, s = 3 km. If the answer needs rounding, round it to three significant digits. r = __________ km

Accepted Answer

The answer of θ  is a central angle that cuts...

Question 14

A woman rides a bicycle for 2 hours and travels 26 kilometers (about 16 miles). Find the angular velocity of the wheel if the radius is 30 centimeters. 
If the answer needs rounding, round it to the whole number. __________ rad/min

Accepted Answer

The answer of A woman rides a bicycle for 2...

Question 15

Find θ , if     and ​   and θ  in QIII ​   __________ °

Accepted Answer

The answer of Find θ , if     and...

Question 16

Use a calculator to find   Please round the answer to the nearest ten-thousandth.

Accepted Answer

The answer of Use a calculator to find  ...

Question 17

Two cities are approximately 600 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side.   a = 600 miles ​

Accepted Answer

A) 0.14 radians 
B) 0.135 radians 
C) 0.15 radians 
D) 0.145 radians 
E) 0.13 radians 
A) 0.14 radians 
B) 0.135 radians 
C) 0.15 radians 
D) 0.145 radians 
E) 0.13 radians

Evaluate the expression when x is . Use exact values. 3 cos 6 x

Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s . cm, cm

Arc length The minute hand of a clock is 1 centimeter0 long. How far does the tip of the minute hand travel in 35 minutes? Round to three significant digits.

For the problem below, θ is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 2, r = 5 inches.

Find the area of the sector formed by central angle θ = 2.8 in a circle of radius r = 5 inches.

Find the radian measure of angle θ , if θ is a central angle in a circle of radius r , and θ cuts off an arc of length s . cm, cm θ = __________ radians

Use a calculator to find θ to the nearest tenth of a degree, if and with θ in QIII

A lawn sprinkler is located at the corner of a yard. The sprinkler is set to rotate through 90 and project water out 53 feet. What is the area of the yard watered by the sprinkler? If the answer needs rounding, round it to three significant digits. A = __________ feet²

Point P sweeps out central angle θ as it rotates on a circle of radius r . Find the angular velocity of point P . Round to the nearest thousandth.

Draw the following angle in standard position and then name the reference angle.

Use the unit circle to find the six trigonometric functions of 240°.

θ is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 160°, s = 3 km. If the answer needs rounding, round it to three significant digits. r = __________ km

A woman rides a bicycle for 2 hours and travels 26 kilometers (about 16 miles). Find the angular velocity of the wheel if the radius is 30 centimeters. If the answer needs rounding, round it to the whole number. __________ rad/min

Find θ , if and and θ in QIII __________ °

Use a calculator to find Please round the answer to the nearest ten-thousandth.

Two cities are approximately 600 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side. a = 600 miles

The Six Trigonometric Functions

Right Triangle Trigonometry

Graphing and Inverse Functions

Identities and Formulas

Equations

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Complex Numbers and Polar Coordinates

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Exam 3: Radian Measure