Sunday, January 11, 2009

Converting Degrees to Radians and Radians to Degrees

Yesterday we learned about degrees and radians: two ways to measure an angle.

Today we will learn how to convert one measure to the other.

A full circle is equal to 360 degrees which is equal to 2(pi)

Thus 360 degrees = 2(pi) radians

dividing by 360 we get

1 degree = 2(pi)/360


1 degree = (pi)/180


1 radian = 180/(pi) degrees

How many radians equal 150 degrees?

To find this we multiply by pi/180 thus

150*(pi/180) = 5(pi)/6 radians

So 150 degrees equals 5(pi)/6 radians. Radians are typically written as fractions since pi is irrational. Irrational means it has an infinite number of decimals.


Now let us convert radians to degrees, how many degrees are in 7(pi)/12 radians?

To find this we multiply the radians by 180/pi and so we get

7(pi)/12 * 180/pi = 105 degrees

So there are 105 degrees in 7(pi)/12 radians.