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