Trigonometry (graph of sine)

Question

Why is the phase shift: C/B for the function of the form y=Asin(Bx-C)

Answer 1

Normally, the general model for a sine curve is:

y = Asin(B(x-φ)) + D

A = amplitude

B = 2π/period

φ = the phase shift right (Horizontal move right)

D = the Vertical shift (zero for this case)

To put Bx-C into the same format above, Bx-C = B(x-C/B) = B(x-φ))

So the phase shift right, φ = C/B