what is the exact value of sin(-5π/3)? 1/2 -√3/2 √3/2 -1/2

Explanation:

Step1: Use the property of sine function

We know that $\sin(-\alpha)=-\sin(\alpha)$. So, $\sin\left(-\frac{5\pi}{3}\right)=-\sin\left(\frac{5\pi}{3}\right)$.

Step2: Rewrite the angle

Rewrite $\frac{5\pi}{3}$ as $2\pi-\frac{\pi}{3}$. Then $\sin\left(\frac{5\pi}{3}\right)=\sin\left(2\pi - \frac{\pi}{3}\right)$. Since $\sin(2\pi-\theta)=-\sin\theta$, we have $\sin\left(2\pi - \frac{\pi}{3}\right)=-\sin\left(\frac{\pi}{3}\right)$.

Step3: Find the value of $\sin\left(\frac{\pi}{3}\right)$

We know that $\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}$.

Step4: Calculate the original - value

Since $\sin\left(-\frac{5\pi}{3}\right)=-\sin\left(\frac{5\pi}{3}\right)$ and $\sin\left(\frac{5\pi}{3}\right)=-\sin\left(\frac{\pi}{3}\right)$, then $\sin\left(-\frac{5\pi}{3}\right)=-(-\frac{\sqrt{3}}{2})=\frac{\sqrt{3}}{2}$.

Answer:

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