Write Trig Function Given Features

Question

Write a sine function that has an amplitude of 4, a midline of 3 and a frequency of 4

Answer 1

y = Asin(Bx-C) + D

D is midline. A is amplitude. Period is 2π/|B| (More useful for graphing and shows the effect of B). Strictly speaking, the frequency is the inverse of period: f = |B|/(2π), but a lot of math texts say frequency when they mean angular frequency which is rad/s vs. cycles/sec. The angular frequency ω = 2πf (2π rads/cycle) or just |B|. Finally the function is translated to the right C/B (to the left if C/B is negative)

Take care.