Why do we use radian instead of degree in "higher mathematics", for example, in calculus?

Question

ipwnbunnies · Answer

Yes.

ipwnbunnies · Answer

Usually starting with Precalculus.

anonymous · Answer

But why?

ipwnbunnies · Answer

I think because degrees is a "false" unit, like it's manmade.
Radians real with pi, which is a real ratio of circumference-to-diameter of a circle. It has a connection, and I don't have the time capacity or patience to talk about it lol.

ipwnbunnies · Answer

Radians deal with pi*

aayushi.somani · Answer

radian is an SI unit and degree is an artificial unit.! if u use degree in calculation is it quit difficult to relate anything.

anonymous · Answer

One good reason could be that radians are much more convenient than degrees. Let's say you have a circle of radius R. If you take a section of X radians, the length of the arc is simply equal to X*R. For degrees, it is $$X*R \div 360$$. That is much messier than simple radians

anonymous · Answer

So, it's for geometric purposes, right?

zehanz · Answer

If you draw graphs of sines or cosines, it is much more convenient to use radians, because they are just numbers. We always like the same units along both axes. If you use degrees instead of radians AND take as unit 1cm along both axes, you will have to make the graph of the sine function 360 cm long (x-axis) while it goes up and down only 1 cm...