Question

find the period and graph the function.
$y = - \frac{1}{7} \tan x$
period = rad

Explanation:

Step1: Recall the period formula for tangent function

The general form of the tangent function is \(y = A\tan(Bx - C)+D\). The period of the tangent function \(y = A\tan(Bx - C)+D\) is given by the formula \(T=\frac{\pi}{|B|}\).

Step2: Identify the value of \(B\) in the given function

For the function \(y =-\frac{1}{7}\tan(x)\), comparing it with \(y = A\tan(Bx - C)+D\), we have \(B = 1\).

Step3: Calculate the period

Substitute \(B = 1\) into the period formula \(T=\frac{\pi}{|B|}\). So, \(T=\frac{\pi}{|1|}=\pi\).

Answer:

\(\pi\)