2/25/13 How do we convert between radians and degrees?

How do we convert between Radians and Degrees ?

Reference angle - the smallest angle that the terminal side if the given angle makes with the x- axis

Radians - one radian is the angle subtended at the center of a circle by an arc that is equal length to the radius of the circle
1 radian = 180/pi = 57.2958

-To convert from Radians to degrees;
Example : 2(pi) x 180 / pi
The (pi) cancel each other out and you're left with (2x180) with equals 360 degrees
Example 2 : 5(pi) x 180/12(pi)
The pi cancel each other out then your left (5x180) = 900/12 then your final answer is 75 degrees


To convert from degrees to radians;
 *Always leave in terms of pi when converting to radians

Example :
60/180(pi) = 1/3(pi) reduce ----> (pi)/3
 Example 2 :
45/180(pi) = 11/12(pi) this can not be reduced








Bibliography (images only)
regentsprep.org ,http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm
Radians , mathisfun.com , http://www.mathsisfun.com/geometry/radians.html