How do you evaluate arcsin(-1) without a calculator?

Nov 23, 2016

$\arcsin \left(- 1\right) = - \frac{\pi}{2}$

Explanation:

$\arcsin x$ means the angle whose sine ratio is $x$ i.e. $\theta$ where $\sin \theta = x$.

Hence, $\arcsin \left(- 1\right)$ means the angle whose sine ratio is $- 1$.

As $\sin \left(- \frac{\pi}{2}\right) = - 1$

$\arcsin \left(- 1\right) = - \frac{\pi}{2}$