Question

How do you determine the amplitude, period, and shifts to graph `y=2cos2x`?

Answer 1

amplitude = 2, period `=pi`

Explanation:

The standard form of the `color(blue)"cosine function"` is

`color(red)(bar(ul(|color(white)(a/a)color(black)(y=acos(bx+c)+d)color(white)(a/a)|)))`

where amplitude = |a| , period `=(2pi)/b`

phase shift `=-c/b` and d is vertical shift

here a = 2 , b = 2 , c = 0 and d = 0

amplitude = |2| = 2 and period `=(2pi)/2=pi`