# How do you graph  f(x)=1- cos 3x?

Nov 5, 2015

$y = 1 - \cos 3 x$

$y = A \cos \left[B \left(x - C\right)\right] + D$ ( A being amplitude, B being the period, C being the phase shift, and D being the vertical shift).

$y = \cos \left[\left(3 x\right)\right] - 1$

Two things I can see immediately now that we reorganized the equation is that we have an amplitude of 1 and a vertical shift of -1 (down 1).

Now we will want to find the period using the equation for finding the period for cosines and sin $\frac{2 \pi}{B}$, so the period is $\frac{2 \pi}{3}$. We also see that there is no phase shift. Okay! We have everything we need to graph the equation now.

Amp: 1
Period: (2pi)/3
PS: none
VS: -1