Question

18 multiple choice 1 point find the period of the graph shown below. 2π/3 4π 1/2 π 2π π

Explanation:

Step1: Understand the concept of period

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

Step2: Count the number of cycles in a known interval

From \(0\) to \(2\pi\), count the number of full - cycles. In the given graph, from \(0\) to \(2\pi\), there are \(4\) full - cycles.

Step3: Calculate the period

Let the period be \(T\). If \(n\) is the number of cycles in an interval of length \(L\), then \(nT = L\). Here, \(n = 4\) and \(L=2\pi\). So, \(4T=2\pi\). Solving for \(T\), we get \(T=\frac{2\pi}{4}=\frac{\pi}{2}\)

Answer:

\(\frac{1}{2}\pi\)