Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
They exist because we defined them, I guess. I don’t really know how to answer your first question.
Radians much more convenient and natural for most areas of maths. Beyond simplifying length and area calculations on a circle, properties like the derivative of sin x being cos x, or the limit of sin x / x at 0 is 1 only work when x is expressed in radians. And when so much of maths relies on calculus, you’re pretty sure people will want to go with the choice that’s most elegant.
Of course nothing fully breaks if you insist on using, say, degrees here, but you end up with factors of pi/180 everywhere.
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