What is the frequency of the motion?

Question

The motion of an object is described by the equation:
x=(0.7m) cos(pi*t / 4)
At .07 sec, x = .5968115 m
1. What is the frequency of the motion? (answer in units of Hz)
2. What is the period of the motion? (answer in units of s)

Answer 1

You can figure out the period by asking how long it takes the cosine function to repeat itself, and this happens whenever pi*t/4 is zero, two*pi, 4*pi, etc.
So solve pi*t/4 = 2*pi to find out the first non-zero time that the pattern is repeated. This happens when t = 8 if my math is right.

The frequency is simply 1 over the period, so the frequency is 1/8 Hz