which is an x - intercept of the graph of the function (y = cot(3x))?\n( (\frac{pi}{6},0))\n(…
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( (3pi,0))\n( (6pi,0))
Answer
Explanation:
Step1: Recall cotangent zero - condition
The cotangent function $y = \cot(u)=0$ when $u = \frac{\pi}{2}+k\pi,k\in\mathbb{Z}$. Here $u = 3x$.
Step2: Solve for $x$
Set $3x=\frac{\pi}{2}+k\pi$. Then $x=\frac{\pi}{6}+\frac{k\pi}{3}$. When $k = 0$, $x=\frac{\pi}{6}$.
Answer:
$\left(\frac{\pi}{6},0\right)$ (corresponds to the first option $\left(\frac{\pi}{6},0\right)$ in the given choices)