which is an x - intercept of the graph of the function y = cot(3x)?\n(\\frac{\\pi}{6},0)\n(\\frac{\\pi}{3},0)…

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

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

Answer

Explanation:

Step1: Recall cotangent - x - intercept property

The x - intercepts of (y = \cot(u)) occur when (\cot(u)=0), and (\cot(u)=\frac{\cos(u)}{\sin(u)}), so (\cot(u) = 0) when (\cos(u)=0) and (\sin(u)\neq0). For (y = \cot(3x)), we set (3x=(2n + 1)\frac{\pi}{2}), (n\in\mathbb{Z}), then (x=\frac{(2n + 1)\pi}{6}), (n\in\mathbb{Z}).

Step2: Find the x - intercept from the options

When (n = 0), (x=\frac{\pi}{6}). The x - intercept is of the form ((x,0)), so the x - intercept is ((\frac{\pi}{6},0)).

Answer:

A. ((\frac{\pi}{6},0))