Why is radian the unit for the arguments of the trigonometric functions? Why not degrees for example?
In $\sin (x) \approx x$ for small $x$, can $x$not be given in degrees (ie, from $0$ to $360$)?
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Sine of $x$ degrees is not close to $x$ for small $x$, as your calculator will gladly tell you. – Gerry Myerson Apr 05 '16 at 07:17
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@GerryMyerson : Gerry, somebody told that to the calculator...It was not another calculator.... – Chip Apr 05 '16 at 07:23
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I usually use that degrees are arbitrary, the number 360 could have been anything else and it still would work, meanwhile radians are natural to the circle, no matter what there are $2pi$ radians in any full circle...though I suppose this is hand-wavy – Triatticus Apr 05 '16 at 07:36
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1Related: http://math.stackexchange.com/questions/1339540/why-does-the-derivative-of-sine-only-work-for-radians, http://math.stackexchange.com/questions/720924/why-do-we-require-radians-in-calculus – Hans Lundmark Apr 05 '16 at 08:41