Question

How do you find the amplitude and period of `f(x) = -7 cos(x/2 + pi)`?

Answer 1

Amplitude is `7`
Period is `4pi`

Explanation:

You must use the coefficients in front of `cos` and `x`:
1] Amplitude is `7` (the modulus of the coefficient `-7`), in this case your `cos` oscillates between `+7` and `-7`;
2] For the period you use the `1/2` in front of `x` in the argument of `cos` as:
`period=(2pi)/color(red)(1/2)` so your period will be `4pi=12.6`.
Graphically you can see these values as:
graph{-7cos(x/2+pi) [-9.93, 10.07, -4.27, 5.73]}