Question

How do you find the period, amplitude and sketch `y=cos2pix`?

Answer 1

In `y = acos(b(x - c)) + d`:

•`a` is the amplitude
•`(2pi)/b` is the period
•`c` is the phase shift, or horizontal transformation
•`d` is the vertical transformation

Here, the amplitude is `1`. The period will be `(2pi)/(2pi) = 1`.

At `x = 0`, `y = 1` (a maximum) and at `x = 1/2`, `y = -1` (a minimum).

Use this to get the following graph:

graph{y = cos(2pix) [-10, 10, -5, 5]}

Hopefully this helps!