Question

What is the amplitude, period and the phase shift of `y= 4 sin(theta/2)`?

Answer 1

Amplitude, `A=4`, Period , `T=(2pi)/(1/2)=4pi`, Phase shift , `theta = 0`

Explanation:

For any general sine graph of form `y=Asin(Bx+theta)`,

`A` is the amplitude and represents the maximum vertical displacement from the equilibrium position.
The period represents the number of units on the x-axis taken for 1 complete cycle of the graph to pass and is given by `T=(2pi)/B`.
`theta` represents the phase angle shift and is the number of units on the x-axis (or in this case on the `theta` axis, that the graph is displaced horizontally from the origin as intercept.

So in this case, `A=4`, `T=(2pi)/(1/2)=4pi`, `theta = 0`.

Graphically :

graph{4sin(x/2) [-11.25, 11.25, -5.625, 5.625]}