Question

Write a cosine function that has a midline of y, equals, 4y=4, an amplitude of 22, a period of 2, pi2π, and a horizontal shift of start fraction, 2, pi, divided by, 3, end fraction
3
2π
​
to the left.

Answer 1

Interpreting the midline y = 4, amplitude = 2, period = 2π, and a horizontal shift 2π/3 to the left:

Period 2π gives B = 2π/(period) = 2π/(2π) = 1. A left shift by 2π/3 means replace x with x + 2π/3.

So one convenient form is
y = 4 + 2 cos(x + 2π/3).

(If you actually meant amplitude = 22, replace the 2 by 22: y = 4 + 22 cos(x + 2π/3).)