Why is the range of inverse trigonometric functions defined in this way? My question is really simple, why is the range of the $\sin^{-1}(x)$, $\cos^{-1}(x)$ and $\tan^{-1}(x)$ defined as $[-\pi/2,\pi/2]$, $[0,\pi]$ and $[-\pi/2,\pi/2]$ respectively? Is there some particular reason? We could choose another range for each inverse trigonometric function. For example, we can pick $[0,\pi]$ to be the range of $\sin^{-1}x$.
EDIT
I've understood why the range of the sine and cosine has to be $[-\pi/2,\pi/2]$ and $[0,\pi]$ respectively. I'm still wondering why can't we define the range of the tangent as $[0,\pi]$

Inverse trigo functions are nothing but angles . Now trigo functions are periodic over $2π$ so there ranges are such also range of tan is $[-π/2,π/2]$ hope i have intrtpreted it correctly.
