Question

What is the amplitude of `y=cos2x` and how does the graph relate to `y=cosx`?

Answer 1

For `y=cos(2x)`, `Amplitude=1` & `Period=pi`
For `y=cosx,Amplitude =1` & `Period=2pi`
Amplitude remains the same but perio halved for `y=cos(2x)`
`y=cos(2x)`
graph{cos(2x) [-10, 10, -5, 5]}
`y=cos(x)`
graph{cosx [-10, 10, -5, 5]}

Explanation:

`y=a*cosx(bc-c)+d`
In given equation `y=cos(2x)`
`a=1,b=2,c=0` & `d=0`
`:.Amplitude=1`
`Period=(2pi)/b=(2pi)/2=pi`

Similarly for Equation `y=cosx`,
`Amplitude=1` & `Period=(2pi)/b=(2pi)/1=2pi`

Period halved to `pi` for `y=cos(2x)` as can be seen from the graph.