Question

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

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Answer 1

Explanation:

Comments

You need to get the radian measure of the circle.

The radian measure of the entire circle is 2 * pi

To get the radian measure of 1/4 of the circle, just divide by 4.

2 pi / 4 = pi/2

The central angle is = to 1/4 of the circumference of the circle.

So the central angle is also pi/2

Answer: pi/2

Answer 2

Explanation:

The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be
`2\pi` since the circumference of any circle is
`2\pi r` except r is 1 so the length is just
`2\pi`. So if you take 1/4 of this you get
`(2\pi)/(4)` which can be simplified to
`(\pi)/(2)`