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

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SOLUTION

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

STEP 1: Write the given function

[tex]f(x)=\cos (4x)[/tex]

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;

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

Hence, the period of the function is:

[tex]\frac{\pi}{2}[/tex]

View image TyheemO557381
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