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Using Degrees and Radians

When finding angles using SIN, COS, and TAN, you have a few different options on how to calculate that angle. Most of the time, we refer to angles in degrees. (A full-circle being 360 degrees.) However, there are different ways to measure the same angle!

Radians: There are 2pi radians in 360 degrees. Technically speaking, the definition of a radian is the angle where the arc of a circle has the same length as the radius of the circle. The graphic below describes this visually.

You usually won't be converting individual degrees to radians (but if you do, 1 degree is roughly equal to .0175 radians), so here is a graphic of many degree to radian conversions, covering the entire 360 degree spectrum.

In the above graphic, each segment is represented by: { degrees, radians }.

 

 

Grads
We haven't actually heard of anyone using this type of measurement lately, but if you happen to find yourself in need of a conversion, 360 degrees (or 2pi radians) is equal to 400 grads. Another method, to calculate grads is Grads = Radians * 200 / pi.

 

Those are the three measurements you may encounter; although you likely will not come across the grads unit of measurement, you can impress all your friends by telling them how many grads are in their answers! Select another topic from the Math Lesson Center!


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