Answer:
y = 4sin [(1/2)t - (4/3)π ] - 2
Step-by-step explanation:
For this question, do not be intimidated by the terminology, just realize the following:
for y = a sin [ (2π/T) t ]
a = amplitude = given as 4
T = period = given as 4π
phase shift is simply horizontal shift, positive values means the graph moves by that amount to left and negative values means the graph moves to the right.
vertical shift ... is well a shift vertically. positive values move the graph up vertically and negative values move the graph down vertically.
so... if we start with the basic formula:
y = a sin [ (2π/T) t ]
given a = 4 and T = 4π (substitute these values into the formula)
y = (4) sin [ (2π/4π) t ] = (4) sin [ (1/2) t ]
y = 4sin [(1/2)t ]
Now for the shifts:
given phase shift, aka horizontal shift is -(4/3)π, equation becomes
y = 4sin [(1/2)t - (4/3)π ]
given vertical shift is -2, the equation simply becomes
y = 4sin [(1/2)t - (4/3)π ] - 2
