Question

How do you find the amplitude and period of `f(t)= -2 cos(3t)`?

Answer 1

Have a look at the numerical factors in your function:

Explanation:

The amplitude is given by the number `2` in front of your `cos` so that your function will oscillate between `+2` and `-2`;
The period can be found using the `3` inside the argument of `cos` as:
`period=(2pi)/color(red)(3)~~2.1rad` so your function repeats itself every `2.1` rads.
Graphically you can see these properties:
graph{-2cos(3x) [-11.25, 11.25, -5.63, 5.62]}