Radians vs degree mode

Question

When it comes to trig, how do I know when to use degree mode or radians mode? I know for elevation/depression problems I have to put my calculator in degrees mode, but why do we do that?

Answer 1

Hi Rawda,

While the math problem should tell you when to use radians and degrees, the reason why you see two different measurements for angles depends on the context of what you are trying to evaluate as well.

Radians is a more natural way of calculating angles. It is dimensionless, and secondly, it uses the length of the radius to measure how far you're going around the circle. You will find it primarily used in calculus and beyond.

To further describe this relationship, 1 radian is the angle created at the center of a circle and the corresponding arc that is equal to the length of the circle’s radius. If you continued to bend the radius along the arc of the circle, you would find that approximately 6 lengths (6.28, or 2π to be exact) would get you all the way around the circle. Because there is a distinct ratio between angle and arc length, it can make calculations much easier.

Radians should also be used when you are examining objects in circular motion or going along a circular path for example.

Degrees is made up by taking a full circle and dividing into 360 equal wedges so to speak, which is why when you first learn about angles, this unit is used as it's much easier to understand. It also helps drawing objects a lot easier. For example, we could take a protractor and pretty quickly create a 30/60/90 degree right triangle with it. There are theories behind why it was divided into 360 initially, including an old ancient calendar that divided a year into 360 days.

Let me know if that helps explain the why.

Thanks.

Answer 2

If the question has degrees in it, use degrees mode. If the question mentions radians, use radians mode.

Examples:

30 degrees is degrees mode.

pi/2 radians is radians mode.