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

Mar 14, 2018

Explanation:

For our situation of ${\sin}^{-} 1 \left({\sin}^{-} 1 \left(- \frac{\pi}{3}\right)\right)$, we are asking ourselves: $\text{In our unit circle definition, what angle gives us the hight of}$ -pi/3?

Just note here that $- \frac{\pi}{3} \approx - 1.0471975511965976$

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.