= Inverse trigonometric functions
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= Inverse trigonometric function
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The <inverse trigonometric functions> invert <trigonometric functions> on branches where they are one-to-one. Standard real ranges are $[-\pi/2,\pi/2]$ for $\arcsin$, $[0,\pi]$ for $\arccos$, and $(-\pi/2,\pi/2)$ for $\arctan$. Thus $\arcsin(1/2)=\pi/6$ but $\arcsin(\sin(5\pi/6))=\pi/6$: the inverse returns the selected branch. The notation $\sin^{-1}x$ usually means $\arcsin x$, not $1/\sin x$. Implicit <differentiation> gives $(\arcsin x)'=(1-x^2)^{-1/2}$ for $|x|<1$.
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