hello
the answer to the question is:
y = a tan(bx – c) + d
a = 1, b = 1, c = π/2
the midline is y = d, so y = 0 and there's no vertical shift
the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1
the period is:
T = π/b ----> T = π
the phase shift is:
PS = c/b ----> PS = π/2
and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude