Converting Angles
Coterminal Angles
Arc Length
Sector Area
Linear Speed
Angular Speed
100
How many degrees and radians are in a circle?
360^o and 2pi
100
What is the definition of a coterminal angle?
Two angles that start on the initial side and have a common terminal side. They start and end in the same position no matter the direction or number of rotations.
100
Find the arc length. Leave your answer in terms of pi
(7pi)/2
100
Find the area of the sector. Round to one decimal.
519.5m^2
100
Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.
5654.9 in/min
100
If you know how fast a wheel is turning in revolutions per minutes, what do you multiply by the find angular speed?
2pi
200
What is (11pi)/6 in degrees?
330^o
200
Determine the quadrant in which the coterminal angles of
283^o
end.
IV
200
If the diameter of a circle is 18m and the central angle is pi/3 , find the arc length to two decimal places.
9.42m
200
Find the sector area outlined in bold.
74.2m^2
200
The wheels of a car have radius 11 in. and are rotating at 600 rpm. Determine the speed of the car in miles/hour to the nearest tenth.
39.3 mph
200
A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.
282.7 rad/min
300
Convert 295.8^o to degrees, minutes, seconds.
295^o48^'
300
Find the coterminal angle between 0 and 2pi for (33pi)/12
(3pi)/4
300
Find the arc length of the bolded arc.
73.3 miles
300
If Pacman's mouth, when open is 70^o and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?
161.97mm^2
300
A car tire has a diameter of 14 inches and is spinning at a of 10 revolutions per second. What is the linear speed in miles per hour?
24.99mph
300
Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave your answer in terms of pi
720 pi
rad/min
400
Write the following angle measures in decimal degree form.
182^o 57^' 93^"
182.976^o
400
Find a positive and negative coterminal angle of -380^o
Possible Positive Answers:
320^o, 680^o
Possible Negative Answers:
-740^o, -40^o
400
An intercepted arc has a length of 19 yards. If the radius is 4 yards, find the measure of the central angle in radians and degrees.
19/4 radians
272.2 degrees
400
Find the area of the shaded sector of the circle. Leave in terms with pi 
(175pi)/4
400
A woman is riding a bicycle whose wheels are 30 inches in diameter. If the wheels rotate at 250 revolutions every 2 minutes, find the speed at which she is traveling in mi/hr.
11.16 mph
400
Dan and Ella are riding a Ferris Wheel. Dan observes that it takes 20 seconds to make a complete revolution. Their seat is 25 feet from the axle of the wheel.
What is their angular velocity in radians per minute?
18.85 rad/min
500
Convert -0.355 radians to degrees, minutes, seconds.
-20^o 20^' 24^('')
500
Find a positive and negative coterminal angles with (17pi)/4
Possible Positive Angles:
(25pi)/4, (9pi)/4, pi/4
Possible Negative Angles:
(-7pi)/4, (-15pi)/4
500
Milford, Connecticut has a longitude of 73.0640^o W and Denver, Colorado has a longitude of 104.9903^o W . With earth having a radius of about 3,959mi find the distance between Milford and Denver.
2206.03mi
500
The sector of a circle has a central angle of 144 degrees and an area of 70.7 square meters. Find the radius of the circle.
7.5m
500
The earth rotates about its axis once every 23 h 56 min 4 secs, and the radius of the earth is 3960 mi. Find the linear speed of a point on the equator in mi/hr.
1039.57mph
500
In order for a lawn mower blade to cut grass, it must strike with a speed of at least 900 inches per second. If the innermost part of the cutting edge is 6 inches from the center of the blade, how many radians per second must the blade turn?
150 rad/sec