Question

find the exact value.

\\( \sin \frac { - 4 \pi } { 3 } \\)

type + or -

? \frac { \sqrt { } } { }

Explanation:

Step1: Use the property of sine function

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

Step2: Rewrite the angle

$\frac{4\pi}{3}=\pi+\frac{\pi}{3}$. Then, using the formula $\sin(\pi + \beta)=-\sin\beta$, we have $-\sin\frac{4\pi}{3}=-(-\sin\frac{\pi}{3})$.

Step3: Find the value of $\sin\frac{\pi}{3}$

We know that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$.

Answer:

$+\frac{\sqrt{3}}{2}$