Question

How do you find the amplitude and period of `y = cos 4x`?

Answer 1

They can be determined by looking at the coefficients and their location.

Explanation:

Let's look at this equation:

`y = Acos(Bx)`

The `A` and `B` coefficients can tell us what the amplitude and period are.

First, `A` tells us what the amplitude is. For example, the amplitude of `y = 2cos(x)` would be simply `2`.

Second, `B` tells us what the period is. In this case, we have to divide the normal period by `B` in order to find the period.

For example, the period of cosine is `2pi`. Therefore, the period would be `[2pi]/B`

For your specific question, `y = cos4x`, the amplitude would be `1` and the period would be `[2pi]/4`, or `pi/2`.

NOTE: I wanted to mention to be careful when finding the period of tangent, as the normal period of tangent is `pi`. Therefore, to find the period, you would do `pi/B` instead.