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

or

1 degree = (pi)/180

conversely

1 radian = 180/(pi) degrees


Examples
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.

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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.