Question

determine the period of the following graph.

Explanation:

Step1: Recall the definition of period

The period of a periodic function is the horizontal length over which the function repeats.

Step2: Identify two consecutive corresponding points

Look at the graph. For example, consider the x - values where the function has a maximum (or any other characteristic point). Let's take two consecutive maxima.
Suppose one maximum is at \(x =-\pi\) and the next maximum is at \(x = 3\pi\).

Step3: Calculate the difference

The period \(T\) is given by \(T=3\pi-(-\pi)\). Using the formula \(a - b=a+( - b)\), we have \(T = 3\pi+\pi=4\pi\).

Answer:

$4\pi$