Inverse Trigonometric Functions — Important Questions

$-\sin^{-1}x$

The property states $\sin^{-1}(-x) = -\sin^{-1}x$ because sine is an odd function.

$\pi$

Since $\cos(\pi) = -1$, the principal value $\cos^{-1}(-1) = \pi$.

$\tan^{-1}x$

The domain of $\tan^{-1}x$ is all real numbers and its range is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

$0$

As $x \to \infty$, $\cot^{-1}x \to 0$ because $\cot(0^+) \to \infty$.