Question

Write the equation of a sine or cosine function to describe the graph. Please help I’ve tried but I keep missing something like finding the c/b. Thanks in advance!!!

Answer 1

Since the function starts at it maximum value, let's use a cosine function to represent it:

$f(x)=A+B\cos(C(x+D))$

Since the midline of the periodic function is y = 2, we have A = 2.

The period of the function is 4pi/3, so we have:

$\begin{gathered} T=\frac{2\pi}{C}\\ \\ \frac{4\pi}{3}=\frac{2\pi}{C}\\ \\ \frac{2}{3}=\frac{1}{C}\\ \\ C=\frac{3}{2} \end{gathered}$

Since the function already starts at its maximum value, there is no horizontal phase shift, so D = 0.

The amplitude is 1 (it goes up and down 1 unit from the midline), so we have B = 1.

Therefore the function is:

$f(x)=2+\cos(\frac{3}{2}x)$