Question

find the exact value. tan 2π/3 type + or - ?√

Explanation:

Step1: Determine the reference angle

The angle \(\frac{2\pi}{3}\) is in the second quadrant. The reference angle \(\theta'\) for \(\theta=\frac{2\pi}{3}\) is \(\pi-\frac{2\pi}{3}=\frac{\pi}{3}\).

Step2: Use the tangent function property

In the second quadrant, \(\tan\theta<0\). And \(\tan\frac{\pi}{3}=\sqrt{3}\). So \(\tan\frac{2\pi}{3}=-\tan\frac{\pi}{3}\).

Answer:

\(-\sqrt{3}\)