Question

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

Answer 1

`y=1-cos3x`

`y=Acos[B(x-C)]+D` ( A being amplitude, B being the period, C being the phase shift, and D being the vertical shift).

`y=cos[(3x)]-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 `(2pi)/B`, so the period is `(2pi)/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