Question

which is an x - intercept of the graph of the function y = cot(3x)?
(π/6,0)
(π/3,0)
(3π,0)
(6π,0)

Explanation:

Step1: Recall x - intercept definition

The x - intercepts of the function \(y = f(x)\) occur when \(y = 0\). So for \(y=\cot(3x)\), we set \(\cot(3x)=0\).

Step2: Recall cotangent property

We know that \(\cot\theta=\frac{\cos\theta}{\sin\theta}\), and \(\cot\theta = 0\) when \(\cos\theta = 0\) and \(\sin\theta
eq0\). So we set \(3x=\frac{\pi}{2}+k\pi\), where \(k\in\mathbb{Z}\) (because \(\cos t = 0\) when \(t=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}\)).

Step3: Solve for x

Dividing both sides of \(3x=\frac{\pi}{2}+k\pi\) by 3 gives \(x=\frac{\pi}{6}+\frac{k\pi}{3}\).
When \(k = 0\), \(x=\frac{\pi}{6}\). The x - intercept is of the form \((\frac{\pi}{6},0)\).

Answer:

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