Converting Degrees to Radians
How many complete rotations does the minute hand of a clock make as it moves from 12:00 noon to 4:00 p.m.? rotations
4
How many radians is -135°?
-3/4 pie
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. inches
125.7
An angle measures 7/9pie radians. What is the degree measure of the angle?
140⁰
A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of 2pie/3
20.94 inches
An angle measures 4.3 radians. To the nearest degree, what is the measure of the angle? degrees
246
What is the approximate length of arc s on the circle?
52.36 in.
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? inches
75
What is the total radian measure of the angle the minute hand travels in 4 full rotations?
8 pie
Compare an angle having a measure of 120° with that of an angle whose measure is 5pie/6 radians. Explain your reasoning.
Because the rotation from 12 to 4 is one-third of a complete rotation, it seems reasonable to assume that the hour hand is moving continuously and has ... If you recall from the last lesson, we defined a radian as the length of the arc the measure of an angle θ in radians is defined as the length of the arc cut off.