2. -/1 points details my notes oscat1 8.1.034. let f(x)=sin(x). let f(x)=√2/2 on 0, 2π). find all values of…

Explanation:

Step1: Recall sine - value knowledge

We know that $\sin(x)=\frac{\sqrt{2}}{2}$ has well - known solutions in the unit circle.

Step2: Find solutions in $[0, 2\pi)$

In the interval $[0, 2\pi)$, $\sin(x)=\frac{\sqrt{2}}{2}$ when $x = \frac{\pi}{4}$ (in the first quadrant) and $x=\frac{3\pi}{4}$ (in the second quadrant) since $\sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ and $\sin(\pi - \frac{\pi}{4})=\sin(\frac{3\pi}{4})=\frac{\sqrt{2}}{2}$.

Answer:

$\frac{\pi}{4},\frac{3\pi}{4}$