## Trigonometry (11th Edition) Clone

$\sin^{-1}(-\sqrt{2})$ is not defined.
Inverse Sine Function $y=\sin^{-1}x$ or $y=$ arcsin $x$ means that $x=\sin y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$. ------------------- Since $-\sqrt{2} < 1$, there is no y such that $\sin y=\sqrt{-2}$ $y=\sin^{-1}(-\sqrt{2})$ is not defined. $\sin^{-1}$or arcsin is the inverse of $\sin,$ so its domain must be the range of sine. The range of sine is $[-1,1]$ and $-\sqrt{2}\not\in [-1,1] )$