Question

period of cos(x-pi)

Answer 1

the period of \(\cos(bx+c)\) is \(\frac{2\pi}{b}\)
in your case \(b=1\)

Answer 2

A period, which we can call T, is when the period repeats itself again. With math symbols it looks like:

f(x)=f(x+T)

So this means that if you have something like sin(x) you can see that if we plug in x+T everywhere we have x we will get:

sin(x+T)

and since the period of a sine function is 2pi, we can plug it in for T...

sin(x+2pi)

and since sine looks like this: So you can see that if we start 2pi later we have the exact same graph!

sin(x+2pi)=sin(x)

So it's a similar thing here. Play around with your graphing calculator to see for yourself.