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

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

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

Add (\frac{5\pi}{6}) to both sides: (x=k\pi+\frac{5\pi}{6}). When (k = 0), (x=\frac{5\pi}{6}).

Answer:

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