Question

What is the graph of `y=cos^2 x`?

Answer 1

Here is the graph:
graph{y=(cosx)^2 [-10, 10, -5, 5]}

Remember the double-angle formula for cosine:
`cos(2x) = 2cos^2(x) -1`

Add one to both sides:
`cos (2x) + 1 = 2cos^2(x)`

Divide both sides by two:
`1/2cos(2x) +1/2 = cos^2(x)`

You now have a standard cosine equation with
Amplitude = `1/2`

Period = `pi`

Vertical Shift = up by `1/2`