Question

How do you find the amplitude and period of f(x)=-4sin(7x+2)#?

Answer 1

Amplitude is `4`
Period is `2/7pi`

Explanation:

You must use the coefficients in front of `sin` and `x`:
1] Amplitude is `4` (the modulus of the coefficient `-4`), in this case your `sin` oscillates between `+4` and `-4`;
2] For the period you use the `7` in front of `x` in the argument of `sin` as:
`period=(2pi)/color(red)(7)` so your period will be `2/7pi=0.897~~0.9`.
Graphically you can see these values as:
graph{-4sin(7x+2) [-9.93, 10.07, -4.27, 5.73]}