Question

How do you find the amplitude, period, and shift for `y=5 sin x`?

Answer 1

For any general sine graph of the form `y=Asin(Bx+theta)`,
`A=` amplitude and represents the maximum vertical displacement from the equilibrium position.
`T=(2pi)/B` is the period and represents the number of units on the x-axis for a full cycle to be completed.
`theta` is the phase angle shift and represents the number of units on the x-axis that the graph is displaced horizontally from cutting at the origin.

So in this particular case, the amplitude `A=5`, the period `T=(2pi)/1=2pi` and the phase angle shift `theta=0`.

Consequently the graph of the function looks as follows :

graph{5sinx [-11.25, 11.25, -5.625, 5.625]}