Question

How do you find the period and amplitude for `y=1/4 cos((2x)/3)`?

Answer 1

I found:
`"Amplitude"=1/4`
`"period"=3pi`

Explanation:

The amplitude will be the number in front of your `cos`, i.e., `1/4`; this tells you that your function oscillate between `1/4` and `-1/4`.
The period is a bit more tricky; you use the number in front of the `x` of the argument of `cos`, i.e., `2/3`; let us call it `n`, so we have:
`"period"=(2pi)/n=(2pi)/(2/3)=3pi` this means that your function makes a complete oscillation in `3pi` radians.

Graphically:
graph{(1/4)cos(2x/3) [-10, 10, -5, 5]}