I recently learned that in order to graph any trig function you need to factor the period out of the phase shift. Can someone explain why? I think this has something to do with the multiple x intercepts but I am not sure.

Answer 1

Note that if you have sin(kx-b) that gives you little information about the phase shift. You will need to plot a bunch of points to see the graph.

But, if you write that as sin( k(x-b/k) ) you can see immediately that the shift is (b/k) to the right. You can still see that the period is 2π/k, but now you can also see the shift.

Answer 2

excellent response.