Question

How do you find the amplitude and period of `y =cos6x`?

Answer 1

I foun:
Amplitude `A=1`;
Period `pi/3`

Explanation:

Your equation is in the form `y=Acos(kx)`
Where:
`A=`amplitude; in your case `A=1`;
`k=(2pi)/(period)`; so that in your case:
`period=(2pi)/k=(2pi)/6=pi/3`.
Your `cos` function will oscillate between `+1 and -1` and complete an entire oscillation, say, between zero and `pi/3=1.05`.
Graphically you can see this by plotting your `cos`:
graph{cos(6x) [-3.895, 3.9, -1.95, 1.947]}