find the exact value of sin(-3π/4). sin(-3π/4) =

Answer:

$-\frac{\sqrt{2}}{2}$

Explanation:

Step1: Use sine - angle property

$\sin(-\alpha)=-\sin\alpha$, so $\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})$.

Step2: Rewrite $\frac{3\pi}{4}$

$\frac{3\pi}{4}=\pi - \frac{\pi}{4}$, so $\sin(\frac{3\pi}{4})=\sin(\pi-\frac{\pi}{4})$.

Step3: Apply sine - difference formula

Since $\sin(\pi - \theta)=\sin\theta$, then $\sin(\pi-\frac{\pi}{4})=\sin\frac{\pi}{4}$.

Step4: Recall sine value of $\frac{\pi}{4}$

We know that $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step5: Find the original value

Since $\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})$ and $\sin(\frac{3\pi}{4})=\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$, then $\sin(-\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}$.