Question

How do you graph `y = cos2x`?

Answer 1

This is a cossine function that gives you a graph similar to the "normal" cosine with amplitude `1` BUT period of `pi` only .

Explanation:

This is a cosine function with amplitude equal to `1` (it comes from the one "in front" of `cos` that is not written but it is there!) and period obtained from the `2` in front of `x` in the argument as:
`period=(2pi)/color(red)(2)=pi`.

This value of the period tells you that this is not the normal cosine but it is "squeezed" to fit an entire oscillation between `0` and `pi` instead of between `0` and `2pi` as the "normal" cosine.

Graphically:
`y=cos(2x)`
graph{cos(2x) [-10, 10, -5, 5]}

A "normal" cosine would look as:
`y=cos(x)`
graph{cos(x) [-10, 10, -5, 5]}