Radians

You are probably familiar with degrees as a measure of how large an angle is. Another way of describing angles is with radians. As you approach pre-calculus and your upper years of mathematics, degrees will become less and less frequent and radians become the norm. It’s a good idea to get used to them now, especially if you plan on studying mathematics. Degrees work by dividing a circle into 360 equal parts. Radians work the same way, except a circle has 2π radians. π radians equal one half of the circle or 180 degrees, this is important to remember.

How do you convert an angle from degrees to radians? You multiply it by π/180.

The example shows what 45 degrees is in radians. You will see that 45 degrees converted to radians equals π/4.

Note: Make sure you leave it in this form. Don't type it into a calculator which will return a decimal answer. Radians will always be fractional and have a π in the expression.

If you know what an angle is in radians and you want to know what the degrees would be, you multiply the angle by 180/π. 5π radians in degrees will equal 900 degrees.

Your calculator has a pi button, in case it's not handy, pi equals 3.14159265.

Are you ready to try a few conversions of radians to degrees and degrees to radians? Here's a PDF worksheet for you to try.

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