evaluate the expression sin^(-1)(cos(π/3)). give your answer as an exact value question help: video 1 video…

Explanation:

Step1: Find the value of $\cos(\frac{\pi}{3})$

We know that $\cos(\frac{\pi}{3})=\frac{1}{2}$.

Step2: Evaluate $\sin^{-1}(\frac{1}{2})$

Let $y = \sin^{-1}(x)$, then $\sin(y)=x$ and $y\in[-\frac{\pi}{2},\frac{\pi}{2}]$. For $x = \frac{1}{2}$, we have $\sin(y)=\frac{1}{2}$ and $y\in[-\frac{\pi}{2},\frac{\pi}{2}]$, so $y=\frac{\pi}{6}$.

Answer:

$\frac{\pi}{6}$