# What is the equation for the inverse of y = 1/2 Sin x?

Jun 22, 2018

$y = {\sin}^{- 1} \left(2 x\right)$

#### Explanation:

$y = \frac{1}{2} S \in x$

Swap $x \iff y$ and sove for $y$:

$x = \frac{1}{2} S \in y$

$2 x = S \in y$

${\sin}^{- 1} \left(2 x\right) = {\sin}^{- 1} \left(S \in y\right)$

$y = {\sin}^{- 1} \left(2 x\right)$