Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
If you want to know how far a wheel has traveled, it’s the angle of rotation (in radians) times its radius. Every problem involving “rotating without slipping” needs angles in radians.
Also, if you learn a little calculus you’ll run across something called a Taylor’s expansion, which is a way of expressing trigonometric functions as polynomials; e.g., sin(x) = x – x^3 /3! + x^5 /5! -… These functions only work when x is in radians.
To your point, when performing trig functions of angles, it doesn’t really matter if you sin(45°) or sin(pi/4), as long as your calculator is in the right mode. But as soon as you start multiplying angles with other angles or most other math with them, the angles need to be in radians.
I think of it as angles in degrees have units, and angles in radians do not.
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