Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=a \cdot \cos{bx}$ have:
period = $\dfrac{2\pi}{b}$
amplitude = $|a|$
The given function has $a=5$ and $b=120\pi$ thus
period = $\dfrac{2\pi}{120\pi}=\frac{1}{60}$
amplitude = $|5| = 5$
To graph the function, perform the following steps:
(1) With a period of $\frac{1}{60}$, one period of the function is over the interval $[0, \frac{1}{60}]$.
(2) Divide this interval into four parts to obtain the t-values $0, \frac{1}{240}, \frac{1}{120}, \frac{1}{80}, \text{ and } \frac{1}{60}$.
(3) Make a table of values using the t-values above. (Refer to the table below.)
(4) Plot the five points of the table of values then connect them using a sinusoidal curve whose ampliude is $5$.
(5) Repeat the cycle of the graph form one more period, which is $[\frac{1}{60}, \frac{1}{30}]$.
(Refer to the graph in the answer part above.)