Question

This graph represents the function (*) = cos(4x)no-1What is the period of the function?O A 20ocOD

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function

`f(x)=\cos (4x)`

STEP 2: Show the graph

The period of a periodic function is the interval of x-values on which the cycle of the graph that's repeated in both directions lies.

The period can be seen from the image of the graph, this can be calculates as;

`\begin{gathered} (3\pi)/(4)-(\pi)/(4) \\ \mathrm{Apply\: rule}\: (a)/(c)\pm(b)/(c)=(a\pm\:b)/(c) \\ (3\pi-\pi)/(4) \\ \mathrm{Add\: similar\: elements\colon}\: 3\pi-\pi=2\pi \\ =(2\pi)/(4) \\ \mathrm{Cancel\: the\: common\: factor\colon}\: 2 \\ =(\pi)/(2) \end{gathered}`

Hence, the period of the function is:

`(\pi)/(2)`