Question

How do you find the amplitude and period of `y= 1/4 sin x`?

Answer 1

The period of `y = 1/4sin(x)` is `2pi`
The amplitude of `y=1/4sin(x)` is `1/4`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")`(that is `y epsilon [-1/4, +1/4]`)

Explanation:

The period of `sin(x)` is `2pi`
Multiplying `sin(x)` by a constant only stretches the graph vertically by whatever that constant is; it does not change (for example) the points at which `sin(x)` returns to `0`.

As noted above, multiplying `sin(x)` by a constant stretches it's value by that constant.
Since the range of `sin(x)` is `[-1, +1]`
`color(white)("XXXX")`the range of `1/4sin(x)` is `[-1/4, +1/4]`
`rArr` an amplitude of `1/4`