Write equations for each of the following: A cosine function with period 2, amplitude 6, and phase shift 3.

Answer 1

General equation is y = a cos b (x-c) + d

a = amplitude

2π/b is the period, so b = 2π/period

c is the phase shift

d is the vertical shift

So here a = 6, b = 2π/2, c = 3 , d = 0

So y = 6 cos π (x-3)

You can plot this on Desmos (make sure you are working in radians) and check this