Question

evaluate the expression $\sin^{-1}(\cos(\frac{\pi}{4}))$.
give your answer as an exact value
question help: video 1 video 2

Explanation:

Step1: Calculate the value of $\cos(\frac{\pi}{4})$

We know that $\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$.

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

Let $y = \sin^{-1}(x)$, then $y\in[-\frac{\pi}{2},\frac{\pi}{2}]$ and $\sin(y)=x$.
Since $\sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ and $\frac{\pi}{4}\in[-\frac{\pi}{2},\frac{\pi}{2}]$.

Answer:

$\frac{\pi}{4}$