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Radian Measure

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- A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle.

- Consider the circle at the right. Let the radius be given by r.

- Measure an arc on the circle of length r, the radius of the circle.

- Draw a line segment from the center of the circle to point A, and name the central angle θ.

- Angle θ has a measure of 1 radian.

- Now consider a central angle that subtends an arc that is twice the length of the radius.

- Angle α has a measure of 2 radians.

- In general, if a central angle θsubtends an arc of length s, then the radian measure of θis given by …

- Example 1:
- A central angle θsubtends an arc of length 27cm. in a circle of radius 6cm. Determine the measure of θ.

- Notes:
- Radians is sometimes abbreviated rad.
- Sometimes neither radians nor rad is added. In the previous example, we could say that the measure of the angle was 4.5, and the intent would be 4.5 radians.
- If the measure is intended to mean degrees, then the degree symbol will be added.