Question

What is the exact value of the expression `sin^(-1) (sin^(-1)(-pi/3))` ?

Answer 1

Read below.

Explanation:

For our situation of `sin^-1(sin^-1(-pi/3))`, we are asking ourselves: `"In our unit circle definition, what angle gives us the hight of"` `-pi/3?`

Just note here that `-pi/3~~-1.0471975511965976`

The maximum height a point on the unit circle can maintain is `1`. (Similarly, the minimum is `-1`).

No angle value can give you a value less than `-1`.

Therefore, no angle satisfies our requirement.