# How do you plug the inverse sin (-7/3) into the calculator?

Aug 5, 2015

You will need a calculator that can return imaginary results.

#### Explanation:

$- \frac{7}{3}$ is outside the range of sine for real domain. Many calculators will return an "error" or "invalid input".

If your calculator can do this problem, you should be able to plug it in just like you would for inverse $\sin \left(- \frac{3}{7}\right)$

I'm confident that there is a way to do this on a calculator that is not made for it, but it will involve knowing more than I do about sines of imaginary domains.

OK, here is the formula (from wikipedia: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions )

$\arcsin x = i \ln \left(i x + \sqrt{1 - {x}^{2}}\right)$

Of course, you'll still need to find a complex logarithm on your calculator.
But it can be done by hand, so there must be a way of using the calculator to make it easier.