1 / 6

Radian Measure

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.

noam
Download Presentation

Radian Measure

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. 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.

  3. 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.

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

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

  6. 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.

More Related