# How do you evaluate sin^-1(sin((9pi)/10))?

Jul 12, 2016

$\frac{9 \pi}{10}$

#### Explanation:

Successive operations with f and its inverse ${f}^{- 1}$, either way, on

an operand, returns the operand as the result.

Explicitly, if y = f(x), then ${f}^{- 1} f \left(x\right) = x \mathmr{and} f {f}^{- 1} y = y$.

Here, $f = \sin , {f}^{- 1} = {\sin}^{- 1}$ and the operand is $\frac{9 \pi}{10}$.

So, ${\sin}^{- 1} \sin \left(\frac{9 \pi}{10}\right) = \frac{9 \pi}{10}$.