Question

what is $\sin(-\frac{3\pi}{4})$?

Explanation:

Step1: Use the property of sine function

The sine function is odd, so \(\sin(-x)=-\sin(x)\). Then \(\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})\).

Step2: Find the value of \(\sin(\frac{3\pi}{4})\)

We know that \(\frac{3\pi}{4}=\pi - \frac{\pi}{4}\), and \(\sin(\pi - \alpha)=\sin\alpha\). So \(\sin(\frac{3\pi}{4})=\sin(\frac{\pi}{4})\). And \(\sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\).

Answer:

\(-\frac{\sqrt{2}}{2}\), so the number in the green box is \(2\) and the number in the white box is \(2\).