**Objective**: Define radian measure for angles.

We define

**one radian**(rad) as the central angle of a circle that subtends an arc equal to the length of the radius of the circle.

As you can see, one radian is quite a bit larger than one degree. In fact, one radian is approximately 57.3°. An angle measuring two radians subtends an arc of length two times the radius of the circle, three radians subtends an arc of length 3 times the radius, and so on. In general, the arc length can be expressed as some factor times the radius follows.

It is this factor

*θ*, the ratio of the arc length

*s*subtended by a central angle divided by the radius

*r*of the circle, which defines

**radian measure**of an angle.

For example, consider the circle of radius 2 centimeters in which central angle

*θ*subtends an arc of length 6 centimeters as illustrated below.

The radian measure of the angle is,

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