determine the sign of tan(7π/6) and the quadrant in which it lies. (1 point)\no tan(7π/6) is positive and…

Explanation:

Step1: Find the equivalent angle

First, convert $\frac{7\pi}{6}$ to an angle between $0$ and $2\pi$. We know that $\frac{7\pi}{6}=\pi+\frac{\pi}{6}$.

Step2: Determine the quadrant

Since $\pi<\pi + \frac{\pi}{6}<\frac{3\pi}{2}$, the angle $\frac{7\pi}{6}$ lies in Quadrant III.

Step3: Recall the sign - rule of tangent

The tangent function $y = \tan\theta=\frac{\sin\theta}{\cos\theta}$. In Quadrant III, $\sin\theta<0$ and $\cos\theta<0$. So, $\tan\theta=\frac{\sin\theta}{\cos\theta}>0$ (a negative divided by a negative is positive).

Answer:

$\tan(\frac{7\pi}{6})$ is positive and lies in Quadrant III.