Question

the graph of a trigonometric function is shown. what is the period of this function?

Explanation:

Step1: Recall the definition of period

The period of a trigonometric function is the horizontal length of one complete cycle of the graph.

Step2: Identify two corresponding points on the graph

For example, we can look at the points where the function has the same value and the same behavior (e.g., two consecutive minima or maxima or two consecutive x - intercepts with the same slope). Let's take the minima. One minima is at \(x=-3\pi\) and the next minima is at \(x = 3\pi\).

Step3: Calculate the difference

The period \(T\) is given by \(T=3\pi-(- 3\pi)\)

$$T = 6\pi$$

Answer:

\(6\pi\)