How do we convert between radians and degrees?

Definitions:
     Radian: One Radian is an angle formed at the center of a circle by an arc that is equal in length to the radius of the circle.

Converting Degrees to Radians:
360 Degrees is equal to 2π(pi)

To Find out how many radians are in 90 Degrees we need to set up a ratio.
         90  = Radians
        360        2π
We then multiply degrees by 2π and divide by 360, simplified is:  π  
                                       180

  90   π = 1 π = π
 180         2       2

Converting from Radians to Degrees:

Formula:  Multiply 180

 π    

For Example:

π * 180

6     π  

Cross out the π's because they cancel out each other. 

So you just divide 180 by 6 and that will equal to 30 degrees

Lets Try Some Problems:

Convert to Radians:

1. 60 π  2. 45 π 

   180       180

= 1/3π = π/3    =1/4π = π/4

Convert to Degrees:

     1. 2π*180      = 360 Degrees

             π

     2. 5π * 180    = 900/12 = 75 Degrees

          12    π