# How do you evaluate arcsin(sin((5pi)/3)) ?

Jun 9, 2018

It's $\frac{5 \pi}{3}$.

#### Explanation:

The arcsin function is the inverse function of sin. You can think of it in the same way that taking away a number is the opposite of adding it.

Your question is like asking "What's 5 + 2 - 2?". It's just the same as what you started with - we don't need to figure out what 5 + 2 is because we know that we're just going to take away 2 again, so we know it's 5.

In the same way, we don't need to work out what $\sin \left(\frac{5 \pi}{3}\right)$ is, because we know that we're "undoing" the sin function anyway with the $\arcsin$. (For the record, though, it's $- \frac{\sqrt{3}}{2}$).

Hope this helps :-)