A pendulum's height is modeled by the function h(t) = 4 cos(pi/4*t) + 8 where h is the measure of the pendulum's height in feet and t is the number of seconds since the
maximum height. How many seconds does it take the pendulum to complete one
full swing?

Explanation:

The general cosine template is

y = A*cos(B(t - C)) + D

where in this case

We only really need to worry about the B value. To get the period T, we do the following

T = 2pi/B

T = (2pi)/(pi/4)

T = 2pi * (4/pi)

T = 8

Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).

The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).