Question

How do you use transformation to graph the cosine function and determine the amplitude and period of `y=3cosx`?

Answer 1

The amplitude is `3` and the period is `2pi`

Explanation:

The most general cosine-like function that you can have is

`Acos(\omega x + phi) + b`

where:

• `A`, as a multiplicative factor, affects the amplitude of the wave. The amplitude is exactly `A`.
• `omega` affects the period of the wave. The period is `(2pi)/omega`.
• `phi` is the shift of the wave. It affects the wave by horizontal translation.
• `b` is also a shift, but vertical.

If we want to have

`Acos(\omega x + phi) + b = 3cos(x)`

it means that we have chosen `A=3`, `omega = 1`. `phi=0` and `beta=0`.