what about a phase shift??

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The equation for sin or cos is y=a(bx+c)+d. The period is 2π/b so you can find b first. The phase shift is found by setting bx+c=0. If you know the phase shift and have b from the period you can fill the phase shift in for x and solve for c. Sometimes you can write an equation for a graph without using a phase shift just by changing the function from sin to cos or vice versa. Depends on if the graph crosses through the origin (sin curve) or it might have its max on the y axis (cos curve)