Question

find the period and graph the function.

( y = 4 \tan x )

period ( =quad mathrm{rad} )

Explanation:

Step1: Recall the formula for the period of 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 \(y = 4\tan(x)\), comparing it with \(y = A\tan(Bx - C)+D\), we have \(A = 4\), \(B = 1\), \(C = 0\), and \(D=0\).

Step3: Calculate the period

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

Answer:

\(\pi\)