Question

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

Answer 1

The amplitude is `4` and the period is `2pi`.

Explanation:

Find the amplitude and period of `y=color(red)4sintheta`.

A sine function can be written as `y=Asin(Bx-C)+D`

where `A` is the amplitude

`(2pi)/B` is the period

`C/B` is the phase shift and

`D` is the vertical shift.

This example, `y=4sintheta`, may be be written as
`y=color(red)4sincolor(blue)1theta` where
`A=color(red)4` and `B=color(blue)1`

The amplitude is `color(red)4` and the period is `(2pi)/color(blue)1=2pi`.