how to calculate the phase shift in the formula that has sin in both side?

Question

Given formula

$asin ( x ) = b sin( x + \phi)$

where $a$ and $b$ are constants. I want to calculate $\phi$.

Answer 1

we obtain for $b\ne 0$
$\frac{a}{b}\sin(x)=\sin(x+\phi)$
$\arcsin\left(\frac{a}{b}\sin(x)\right)-x=\phi$