## The General Sine and Cosine Functions

\[f(x)=A+Bsin(Cx-D)\]

and \[g(x)=A+Bcos(Cx-D)\]

.Thse are transformations of the functions

\[f_1(x)=sinx\]

and \[g(x)=cos x\]

.There are altogether four transformations for each funcyion - two

\[x\]

transformations and two \[y\]

transformations.The order of the

\[y\]

transofmations is important, and so is the order of the \[x\]

transfomrations, but either the \[x\]

or \[y\]

transformations may be performed first.1. Scaling in the

\[y\]

direction by a factor \[B\]

then translation in the \[y\]

by an amount \[A\]

.2. Translation in the

\[x\]

direction by an amount \[D\]

then a scaling in the \[x\]

direction by a factor \[C\]

.