Inverse Trigonometric Values

Inverse trig answers are angles, and contest papers ask for them as a multiple of $\pi$: "$\text{Arcsin}(x) = k\pi$ radians, find $k$."

Memorise the principal values. $\text{Arcsin}$ returns angles in $[-\frac{\pi}{2}, \frac{\pi}{2}]$; $\text{Arccos}$ returns $[0, \pi]$; $\text{Arctan}$ returns $(-\frac{\pi}{2}, \frac{\pi}{2})$.

For the reciprocal functions, convert first: $\text{Arccsc}(x) = \text{Arcsin}(1/x)$ and $\text{Arcsec}(x) = \text{Arccos}(1/x)$. So $\text{Arccsc}(-2) = \text{Arcsin}(-\frac{1}{2}) = -\frac{\pi}{6}$, giving $k = -\frac{1}{6}$.