Question

determine the period of the following graph. answer

Explanation:

Step1: Recall the definition of period

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

Step2: Identify one full cycle

Looking at the graph, from \(x = 0\) to \(x = 2\pi\), the graph of the wave - like function (assuming it is a trigonometric function such as \(y = \sin(x)\) or \(y=\cos(x)\) after some transformation) completes one full cycle. For example, if we consider the general form of a sine function \(y = A\sin(Bx - C)+D\), the period \(T=\frac{2\pi}{|B|}\). In the standard case \(B = 1\), and from the visual inspection of the graph (counting the distance between two consecutive peaks or troughs or two consecutive points with the same phase), the distance between \(x = 0\) and \(x = 2\pi\) (where the pattern of the function repeats) gives the period.

Answer:

$2\pi$