# How do you find the exact value of sin^-1[sin(-pi/10)]?

Jul 3, 2015

${\sin}^{-} 1 \left[\sin \left(- \frac{\pi}{10}\right)\right] = - \frac{\pi}{10}$

#### Explanation:

${\sin}^{-} 1 \left[\sin \left(- \frac{\pi}{10}\right)\right]$

A simple way to understand this is from the fact that: $\textcolor{g r e e n}{{\sin}^{-} 1}$ (also denoted byt $\textcolor{g r e e n}{\arcsin}$) is the inverse trig function of $\textcolor{g r e e n}{\sin}$

So if you $\sin$ an angle, you get an real number that lies between $- 1$ and $1$

On the other hand if you ${\sin}^{-} 1$ the answer got previously, you get back the angle.

In the present case, let's say you originally had the angle $- \frac{\pi}{10}$

Now, you when you $\textcolor{red}{\sin}$ it you obtain $\sin \left(- \frac{\pi}{10}\right)$

Then, if you $\textcolor{red}{{\sin}^{-} 1}$ it this time you will get back the angle: $- \frac{\pi}{10}$

That is ${\sin}^{-} 1$ of $\sin \left(- \frac{\pi}{10}\right)$ is $- \frac{\pi}{10}$