Question

choose the correct graph of the function. the amplitude is 2. (simplify your answer. type an exact answer, using π as needed.) the period is. (simplify your answer. type an exact answer, using π as needed.)

Explanation:

Step1: Identify number of cycles in given x - range

From the graph, in the x - range from \(0\) to \(8\pi\), there are 2 full - cycles.

Step2: Calculate the period formula

The period \(T\) of a periodic function is the length of one full - cycle. If there are \(n\) cycles in an interval of length \(L\), then \(T=\frac{L}{n}\). Here, \(L = 8\pi\) and \(n = 2\).

Step3: Calculate the period

Substitute \(L = 8\pi\) and \(n = 2\) into the formula \(T=\frac{L}{n}\), we get \(T=\frac{8\pi}{2}=4\pi\).

Answer:

The period is \(4\pi\)