Question

How do you find the exact value of `sin^-1(-0.5)`?

Answer 1

When asked to evaluate inverse trigonometric functions, first ask yourself, "Is the answer a special angle?"

`sin^-1(-0.5) = sin^-1(-1/2)`

Is there a special angle with `sint = 1/2`?

Yes, `t= pi / 6`.

But we want `sint = -1/2`, so we want an answer in quadrant 3 or 4.

`sin^-1(x)` always gives us a `t` between `-pi/2` and `pi/2`, so we want `t = - pi/6`

`sin^-1(-0.5) = pi/6`