How do you calculate the phase shift?

Question

I'm in the IB program and I'm working on a project and I have a formula in the form y=asin(b(x+c))+d and I don't know how to find c or the phase shift.

Answer 1

c causes the graph to shift right (if c <0) ir left (if c>0),

d causes it to shift up (if d>0) or down (if d < 0)

Answer 2

Assuming you have a graph, look at where the curve peaks. An unshifted sine wave peaks at π/2, and the peaks are 2π apart. Distance between peaks is the wavelength, call it L, and b = 2π/L. To get the peak value, b(x+c) must = π/2, so plug in the x coordinate of the peak (using the x value that does it and is closest to 0) and b, and then solve for c. c should be the phase shift.