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.
You are given:
$\displaystyle -2kt = \sin^{-1}{\left(\frac{v}{k}\right)}$
The only real issue here is the inverse sin, but recall the identity:
$\displaystyle \sin{(\sin^{-1}{(x)})} = x$
So, if we take the sine of both sides we get:
$\displaystyle \sin{(-2kt)} = \sin{\left(\sin^{-1}{\left(\frac{v}{k}\right)}\right)}$
$\displaystyle \sin{(-2kt)} = \frac{v}{k}$
Now we multiply both sides by k and get:
$\displaystyle k\sin{(-2kt)} = v$
And there you go.