Question

In Exercises 59 and \(60,\) show that the function is periodic and find its period. $$f(x)=\cos (60 \pi x)$$

Short answer

The function \(f(x)=\cos (60\pi x)\) is periodic with a period of \(T = 1/60\pi\).

Step-by-step solution

Identify the Function

The given function is \(f(x) = \cos (60\pi x)\), which is a cosine function. Cosine functions are known to be periodic.

Find the Frequency

The formula for a general cosine function is \(\cos(kx)\), where \(k\) is the frequency of the function. In our case, we can see that \(k = 60\pi\). This is the frequency of the function.

Find the Period

The period of a function is given by the inverse of the frequency. Therefore, in this case, the period \(T\) will be \(T = 1/ k\). Subsituting the value of \(k\) from Step 2, we get \(T = 1/60\pi\).