# How do you calculate the sin(sin^-1 (1/3))?

Nov 21, 2015

$\sin \left({\sin}^{-} 1 \left(\frac{1}{3}\right)\right)$ $=$ $\frac{1}{3}$

#### Explanation:

You can just use B.E.D.M.A.S to evaluate this equation, by doing ${\sin}^{-} 1 \left(\frac{1}{3}\right)$, you get $\approx 19.47$.
Then take the $\sin$ of $19.47$ which ultimately gives you the same thing back. $\frac{1}{3}$

Nov 21, 2015

$\frac{1}{3}$

#### Explanation:

$\frac{1}{x} \cdot x = 1$

$x - x = 0$

$\sqrt{{x}^{2}} = x$

${10}^{\log x} = x$

All of these are examples of functions and identities that undo one another. Another example of similar functions are $\sin$ and ${\sin}^{-} 1$.

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

$\sin \left({\sin}^{-} 1 \left(\frac{1}{3}\right)\right) = \frac{1}{3}$