# What is the period and amplitude for f(x) = 2cos(4x + pi) -1?

May 15, 2015

You have the form:
$y =$Amplitude$\cdot \cos \left(\frac{2 \pi}{p e r i o d} x + \ldots .\right)$
Amplitude=$2$
Period=$\frac{2 \pi}{4} = \frac{\pi}{2}$
$+ \pi$ is an initial phase and $- 1$ is a vertical shift.
Note that your $\cos$ is displaced downwards and now oscillates around $y = - 1$! It also starts at $- 1$ as $\cos \left(0 + \pi\right)$.