Radian Measure vs degree measure for central angles
How many radians is -135°? (negative indicates the angle rotated clockwise from the x axis or the initial side)
-3/4 π
Convert -18° to radians. (leave in terms of pi)
-π/10 radians
Use the formula for radian measure to calculate the measure of a central angle in a circle having a radius of 12 cm and intercepting an arc of 21 cm. The angle has a measure of _____ radians.
1.75 or 7/4
If a clock had a minute hand that's 8 inches long, how far will the tip of the minute hand travel when it moves from 12:00pm to 12:15 pm? (ignore the fact the hour hand is moving along with the minute hand)
12.56 inches
The minute hand of the clock is 5 inches long. How far does the tip of the minute hand move in 4 full rotations? Calculate your answer using the pi button on your calculator and round to the nearest tenth of an inch.
125.7
An angle measures 7/9 π radians. What is the degree measure of the angle?
140°
How long is the arc intersected by a 2π/3 radian central angle in a circle with radius 7 feet? (leave pi)
14π/3 feet
How long is the arc intersected by a central angle of π/4 radians in a circle of radius 20 inches. (round to the tenths)
15.7 inches
What is 5π/6 radians converted to degrees? If necessary, round your answer to the nearest degree.
150°
How many degrees are in a semicircle?
180°
To convert from radians to degrees multiply the radian measure by _____ and then divide by _____.
180°/π radians
A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of 2π/3
20.94 inches
What is 4 radians converted to degrees? If necessary, round your answer to the nearest degree.
229°
How many complete rotations does the minute hand of a clock make as it moves from 12:00 noon to 4:00 p.m.?
240
An angle measures 4.3 radians. To the nearest degree, what is the measure of the angle?
246°
There are 360° or _____ radians in a full circle.
2π
A point travels halfway around a wheel with a radius of 1 foot. To the nearest foot, how many feet does it travel?
3 feet
How many degrees are in a full circle?
360°
What is the equivalent radian measure of 540°? (leave pi)
3π radians
Arrange the following from least to greatest. π/2, 60°, 3π/10, 255°, 2π/3.
3π/10, 60°, π/2, 2π/3, 255°
Convert 1 radian to degrees. Round your answer to the nearest degree.
57°
A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. What expression gives the radian measure of the central angle, q?
7/5
A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches. Using 3.14 for π, what is the length of the radius of the circle?
75 inches
How would we convert 8 radians to degrees?
8 * 180°/π
What is the total radian measure of the angle the minute hand travels in 4 full rotations?
8π
How many degrees are in a quarter circle?
90°
What is the formula for the circumference of a circle?
C = 2πr or C = pi (d)
A _____ is an angle formed by two radii.
central angle
Angles can be measured in _____.
degrees or radians
The measure of a central angle that intersects an arc of length equal to the radius is called a(n) ________________
radian
What is the radian equivalent for 180°?
π radians
To convert from degrees to radians multiply the degree measure by _____ and then divide by _______.
π radians/180°
What is 36° converted to radians?
π/5
