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

1 Answer
Dec 7, 2015

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.