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

which is an x - intercept of the graph of the function $y = \\tan(x - \\frac{5\\pi}{6})$?\n$\\left(-\\frac{2\\pi}{3},0\\right)$\n$\\left(-\\frac{\\pi}{3},0\\right)$\n$\\left(\\frac{\\pi}{6},0\\right)$\n$\\left(\\frac{5\\pi}{6},0\\right)$

which is an x - intercept of the graph of the function $y = \\tan(x - \\frac{5\\pi}{6})$?\n$\\left(-\\frac{2\\pi}{3},0\\right)$\n$\\left(-\\frac{\\pi}{3},0\\right)$\n$\\left(\\frac{\\pi}{6},0\\right)$\n$\\left(\\frac{5\\pi}{6},0\\right)$

Answer

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 $\theta = k\pi$, $k\in\mathbb{Z}$. So $x-\frac{5\pi}{6}=k\pi$.

Step3: Solve for x

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

Answer:

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