   Chapter P.4, Problem 80E

Chapter
Section
Textbook Problem

True or False? In Exercises 77-80, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The function y = 3 cos ( x / 3 ) has a period that is three times that of the function y = cos x .

To determine
Whether the given statement “The function y=3cos(x3) has a period that is three times that of the function y=cosx” is true or whether it is false.

Explanation

Consider the given function expressed as,

y=acosx

The period of this function is 2π, which is the standard period of the cosine function.

Now, if the x variable in the function above is altered, then the period of the function will be altered. Consider the modified function given below,

y=acos(xb)

Now, the period of this function will 2bπ.

Note that the coefficient a only denotes the amplitude of the function and thus, it does not alter the period of the function whatsoever.

Now, the period of the function expressed as y=cosx will be 2π

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