which is an x - intercept of the graph of the function $y = \\tan(x - \\frac{5\\pi}{6})$?\n$(-\\frac{2\\pi}{3…

Explanation:

Step1: Recall x - intercept condition

At x - intercept, $y = 0$. So we set $\tan\left(x-\frac{5\pi}{6}\right)=0$.

Step2: Use tangent - zero property

We know that $\tan\theta = 0$ when $\theta = n\pi$, where $n\in\mathbb{Z}$. So $x-\frac{5\pi}{6}=n\pi$.

Step3: Solve for x

$x=n\pi+\frac{5\pi}{6}$. When $n = - 1$, $x=-\pi+\frac{5\pi}{6}=-\frac{\pi}{6}$. When $n = 0$, $x=\frac{5\pi}{6}$.

Answer:

$\left(\frac{5\pi}{6},0\right)$