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# Radian Measure - PowerPoint PPT Presentation

Radian Measure. 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.

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Presentation Transcript
• 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: