Write an equation for the cosine function as described below

Question

1. Amplitude 4
2. Period 180 degrees
3. Reflected in the y-axis
4. phase shift 30 degree to the right

Answer 1

The generic cosine function is f(x) = Acos[B(x - C)] + D where:

A is the amplitude

B is 360°/period

C is the phase shift

D is the vertical shift

In this question, it is important to remember that a function reflected over the y-axis is one where a negative sign is put in front of the "x"

So, since A = 4, B = 360°/180° = 2, C = 30°, and D = 0 as well as we need a negative in front of the x:

f(x) = 4cos[2(-x - 30)]