what is the exact value of $\tanleft(-\frac{pi}{3}\right)$?\n- $sqrt{3}$\n- $\frac{sqrt{3}}{3}$\n…

Explanation:

Step1: Use tangent - angle property

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

Step2: Recall the value of $\tan\frac{\pi}{3}$

The value of $\tan\frac{\pi}{3}=\sqrt{3}$ in the unit - circle or right - triangle trigonometry.

Step3: Calculate $\tan\left(-\frac{\pi}{3}\right)$

Since $\tan\left(-\frac{\pi}{3}\right)=-\tan\frac{\pi}{3}$, substituting $\tan\frac{\pi}{3}=\sqrt{3}$, we get $\tan\left(-\frac{\pi}{3}\right)=-\sqrt{3}$.

Answer:

$-\sqrt{3}$