Equation of A+Bsinx or A+Bcos x From a Graph

Given a graph of the form

\[y=A+B cos x, \: A+B sin x\]

, shown below,

We can easily find

\[A\]

and

\[B\]

\[A=\frac{y_{MAX}+y_{MIN}}{2}=\frac{7+3}{2}=5\]

\[A=\frac{y_{MAX}-y_{MIN}}{2}=\frac{7-3}{2}=2\]

The equation of the graph is

\[y=5+2 cos x\]