Question

What is the amplitude, period and the phase shift of `y=sin(θ - 45°)`?

Answer 1

Given a generic trigonometric function like

`Acos(omega x+phi)+k`, you have that:

1. `A` affects the amplitude
2. `omega` affects the period via the relation `T=(2\pi)/\omega`
3. `phi` is a phase shift (horizontal translation of the graph)
4. `k` is a vertical translation of the graph.

In your case, `A=omega=1`, `phi=-45^@`, and `k=0`.

This means that the amplitude and the period remain untouched, while there is a shift phase of `45^@`, which means that your graph is shifted of `45^@` to the right.