find the exact value.\nsin $\frac{9pi}{4}$\ntype + or -\n? $\frac{sqrt{?}}{?}$

Explanation:

Step1: Rewrite the angle

We know that $\frac{9\pi}{4}=2\pi+\frac{\pi}{4}$. Since $\sin(x + 2k\pi)=\sin(x)$ for any real - number $x$ and integer $k$, then $\sin\frac{9\pi}{4}=\sin(2\pi+\frac{\pi}{4})=\sin\frac{\pi}{4}$.

Step2: Recall the sine value of special angle

The sine of $\frac{\pi}{4}$ is $\frac{\sqrt{2}}{2}$.

Answer:

$+\frac{\sqrt{2}}{2}$