Unit 11.2 - Radian Measure
Find the length of an arc subtended by an angle of radians in a circle of radius 20 centimeters. (Leave answer in terms of π.)
35π
How many complete rotations does the minute hand of a clock make as it moves from 12:00 noon to 4:00 p.m.?
4
The length of an arc is 35 m. If the radius of the circle is 14 m, find the angle measure in terms of degrees. (Leave answer in terms of π.)
(450/π)°
How many radians is -135°?
-3π/4
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 π button on your calculator and round to the nearest tenth of an inch.
125.7
An angle measures 7π/9 radians. What is the degree measure of the angle?
140⁰
Given that a circle has a radius of 7 cm and a minor arc measure of 40°, what it the arc length? (Leave in terms of π.)
14π/9
Find the length of an arc of a circle that has an angle measure of 120 degrees to the center of a circle with 24 cm. (Leave in terms of π.)
16π
A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of 2π/3. (Round to the nearest hundredth, if necessary).
20.94 inches
An angle measures 4.3 radians. To the nearest degree, what is the measure of the angle in degrees?
246°
Convert 3π/2 radians into degrees.
270°
An angle with a full circle rotation measures _____ radians.
2π
A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches. Using 3.14 for pie, what is the length of the radius of the circle in inches?
75 inches
What is the total radian measure of the angle the minute hand travels in 4 full rotations?
8π
Converting Radians to Degrees
d° = θ × 180°/π
Solving for Arc Length
s = rθ where r = radius, and θ = angle measure in radians
Converting Degrees to Radians
θ = d° × π/180°
Radian Measure
θ=s/r where θ = radian measure; s = arc length; and r = radius
An angle with a semicircle rotation measures _____ radians.
π
Convert 45° into radians.
π/4