Question

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

Answer 1

It's `(5pi)/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((5pi)/3)` is, because we know that we're "undoing" the sin function anyway with the `arcsin`. (For the record, though, it's `-(sqrt(3))/2`).

Hope this helps :-)