# Thread: Solving for Variable in an Inverse function

1. ## Solving for Variable in an Inverse function

I am doing this problem and I have to solve for variable v.

-2kt = sin-1(v/k)

the answer is supposedly, v = k sin (-2*k*t)

Please show me the steps. Thank you.

2. You are given:

$-2kt = \sin^{-1}{\left(\frac{v}{k}\right)}$

The only real issue here is the inverse sin, but recall the identity:

$\sin{(\sin^{-1}{(x)})} = x$

So, if we take the sine of both sides we get:

$\sin{(-2kt)} = \sin{\left(\sin^{-1}{\left(\frac{v}{k}\right)}\right)}$

$\sin{(-2kt)} = \frac{v}{k}$

Now we multiply both sides by k and get:

$k\sin{(-2kt)} = v$

And there you go.