Difference between Range and Principal values of trigonometric inverse circular functions.
For, trigonometric inverse circular functions, let talk about $\sin^{-1} x$.
$f:[-\frac{\pi}2, \frac{\pi}2] \to [-1,1] \text{where} f=\sin$ . As $\sin x$ is bijective in the interval. So, $f^{-1}:[-1,1] \to [-\frac{\pi}2, \frac{\pi}2]$ where $f^{-1}=\sin^{-1}$
Hence, range is always $[-\frac{\pi}2, \frac{\pi}2]$ for $\sin^{-1} x$
Then, why there is a term 'Principal value' and 'General value'? By definition $\sin^{-1} x \in [-\frac{\pi}2, \frac{\pi}2]$
Someone please add the correct definition of the above terms. Any suggestion is highly solicited.