Question 1

Find the area of the sector formed by central angle    in a circle of radius r = 3 m. If the answer needs rounding, round it to three significant digits. A = __________ m2

Accepted Answer

Question 2

The current San Francisco cable railway is driven by two large 16-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270° on each sheave. Find the length of cable riding on one of the drive sheaves at any given time.   a = 16 ​

Accepted Answer

A) 38.7 feet 
B) 35.7 feet 
C) 40.7 feet 
D) 37.7 feet 
E) 33.7 feet 
A) 38.7 feet 
B) 35.7 feet 
C) 40.7 feet 
D) 37.7 feet 
E) 33.7 feet

Question 3

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

Accepted Answer

A) 0.989 
B) 0.956 
C) 0.986 
D) 0.936 
E) 0.958 
A) 0.989 
B) 0.956 
C) 0.986 
D) 0.936 
E) 0.958

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 = 315°, r = 5  inches.
​

Accepted Answer

A) s = 29 inches 
B) s = 27.5 inches 
C) s = 31 inches 
D) s = 28.5 inches 
E) s = 29.5 inches 
A) s = 29 inches 
B) s = 27.5 inches 
C) s = 31 inches 
D) s = 28.5 inches 
E) s = 29.5 inches

Question 5

Give the exact value of   .

Accepted Answer

The answer of Give the exact value of  ...

Question 6

Give the exact value of   . ​

Accepted Answer

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

Question 7

Find θ , if   and ​   and  θ in QI ​

Accepted Answer

A) 210   
B) 30   
C) 120   
D) 45   
E) 300   
A) 210   
B) 30   
C) 120   
D) 45   
E) 300

Question 8

Give the exact value of   . ​

Accepted Answer

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

Question 9

Find θ , if   and ​   and  θ in QIV ​

Accepted Answer

A) 300   
B) 60   ​ 
C) 120   
D) 45   
E) 240   
A) 300   
B) 60   ​ 
C) 120   
D) 45   
E) 240

Question 10

Arc length The minute hand of a clock is 1.2 centimeters long. How far does the tip of the minute hand travel in 30 minutes? If the answer needs rounding, round it to three significant digits. __________ centimeters

Accepted Answer

The answer of Arc length The minute hand of a...

Question 11

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

Accepted Answer

A) 5 rad/min 
B) 3.47 rad/min 
C) 3 rad/min 
D) 4 rad/min 
E) 4.43 rad/min 
A) 5 rad/min 
B) 3.47 rad/min 
C) 3 rad/min 
D) 4 rad/min 
E) 4.43 rad/min

Question 12

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of   . Trace the circle to find all values of t between 0 and 2 π  satisfying the following statement. Round your answers to the nearest ten-thousandth.   ​   __________

Accepted Answer

The answer of Graph the unit circle using parametric equations...

Question 13

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 a whole number.   ​

Accepted Answer

A) 102 rad/hr 
B) 114 rad/hr 
C) 109 rad/hr 
D) 108 rad/hr 
E) 156 rad/hr 
A) 102 rad/hr 
B) 114 rad/hr 
C) 109 rad/hr 
D) 108 rad/hr 
E) 156 rad/hr

Question 14

Find the exact value of   .

Accepted Answer

The answer of Find the exact value of  ...

Question 15

A wheel with radius r rotates at 13 rpm. Find v if   ft If the answer needs rounding, round it to the whole number. __________ ft/min

Accepted Answer

The answer of A wheel with radius r rotates at...

Question 16

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

Accepted Answer

The answer of Use a calculator to find θ  to...

Question 17

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of   . Trace the circle to find the sine and cosine of    to the nearest ten-thousandth. ​

Accepted Answer

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

Question 18

A cable railway had a 12-foot-diameter pulley to drive the cable (see the figure). In order to keep the cable cars moving at a linear velocity of 9 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft)​   ​

Accepted Answer

A) 23.2 rpm 
B) 24.5 rpm 
C) 15.3 rpm 
D) 28.1 rpm 
E) 21.0 rpm 
A) 23.2 rpm 
B) 24.5 rpm 
C) 15.3 rpm 
D) 28.1 rpm 
E) 21.0 rpm

Question 19

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

Accepted Answer

The answer of Use a calculator to find θ  to...

Question 20

A wheel with radius r rotates at 6 rpm.  Find v if   ft.  Round to the nearest foot per minute. ​

Accepted Answer

A) 135 ft/min 
B) 151 ft/min 
C) 185 ft/min 
D) 82 ft/min 
E) 63 ft/min 
A) 135 ft/min 
B) 151 ft/min 
C) 185 ft/min 
D) 82 ft/min 
E) 63 ft/min

Find the area of the sector formed by central angle in a circle of radius r = 3 m. If the answer needs rounding, round it to three significant digits. A = __________ m²

The current San Francisco cable railway is driven by two large 16-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270° on each sheave. Find the length of cable riding on one of the drive sheaves at any given time. a = 16

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

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 = 315°, r = 5 inches.

Give the exact value of .

Give the exact value of .

Find θ , if and and θ in QI

Give the exact value of .

Find θ , if and and θ in QIV

Arc length The minute hand of a clock is 1.2 centimeters long. How far does the tip of the minute hand travel in 30 minutes? If the answer needs rounding, round it to three significant digits. __________ centimeters

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth. __________

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 a whole number.

Find the exact value of .

A wheel with radius r rotates at 13 rpm. Find v if ft If the answer needs rounding, round it to the whole number. __________ ft/min

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find the sine and cosine of to the nearest ten-thousandth.

A cable railway had a 12-foot-diameter pulley to drive the cable (see the figure). In order to keep the cable cars moving at a linear velocity of 9 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft)

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

A wheel with radius r rotates at 6 rpm. Find v if ft. Round to the nearest foot per minute.

The Six Trigonometric Functions

Right Triangle Trigonometry

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Complex Numbers and Polar Coordinates

Filters

Exam 3: Radian Measure

Find the area of the sector formed by central angle in a circle of radius r = 3 m. If the answer needs rounding, round it to three significant digits. A = __________ m2

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

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 = 315°, r = 5 inches. ​

Give the exact value of .

Give the exact value of . ​

Find θ , if and ​ and θ in QI ​

Give the exact value of . ​

Find θ , if and ​ and θ in QIV ​

Arc length The minute hand of a clock is 1.2 centimeters long. How far does the tip of the minute hand travel in 30 minutes? If the answer needs rounding, round it to three significant digits. __________ centimeters

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth. ​ __________

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 a whole number. ​

Find the exact value of .

A wheel with radius r rotates at 13 rpm. Find v if ft If the answer needs rounding, round it to the whole number. __________ ft/min

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find the sine and cosine of to the nearest ten-thousandth. ​

A cable railway had a 12-foot-diameter pulley to drive the cable (see the figure). In order to keep the cable cars moving at a linear velocity of 9 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft)​ ​

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

A wheel with radius r rotates at 6 rpm. Find v if ft. Round to the nearest foot per minute. ​

The Six Trigonometric Functions

Right Triangle Trigonometry

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Complex Numbers and Polar Coordinates

Filters

Find the area of the sector formed by central angle in a circle of radius r = 3 m. If the answer needs rounding, round it to three significant digits. A = __________ m²

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

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 = 315°, r = 5 inches.

Give the exact value of .

Find θ , if and and θ in QI

Give the exact value of .

Find θ , if and and θ in QIV

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth. __________

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 a whole number.

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

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find the sine and cosine of to the nearest ten-thousandth.

A cable railway had a 12-foot-diameter pulley to drive the cable (see the figure). In order to keep the cable cars moving at a linear velocity of 9 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft)

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

A wheel with radius r rotates at 6 rpm. Find v if ft. Round to the nearest foot per minute.