what is the exact value of $\tanleft(-\frac{p...
what is the exact value of $\tanleft(-\frac{pi}{3}\right)$?\n- $sqrt{3}$\n- $\frac{sqrt{3}}{3}$\n- $\frac{sqrt{3}}{3}$\n- $sqrt{3}$
Answer
# 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:
$-\sqrt{3}$