\chapter{Trigonometry I}
\section{Graphs of transformed sine and cosine}
Answer the questions.
\begin{enumerate}
\item
What is the difference between a cycle of the sine function and the period?
\item
\(P_1\), \(P_2\), \(P_3\), \(P_4\), \(P_5\) are the five key points in one cycle of the sine
function \(\sin x\) starting at \(x=0\), in increasing order of the \(x\)-coordinate.
Fill the table with either Maximum, Minimum, or At midline:
\[\begin{array}{|c|c|c|c|c|}
P_1 & P_2 & P_3 & P_4 & P_5 \\
\hline
\hspace{10ex} & \hspace{10ex} & \hspace{10ex} & \hspace{10ex} & \hspace{10ex}
\end{array}
\]
\item
State the formula to find the period for a function of form
\[f(x)=A\cos(Bx+C)+k.\]
\item
How are the beginning and end of one cycle found for the function below?
\[f(x)=A\sin(Bx+C)+k\]
\item
\(P_1\), \(P_2\), \(P_3\), \(P_4\), \(P_5\) are the five key points in one cycle of the cosine
function \(\sin x\) starting at \(x=0\), in increasing order of the \(x\)-coordinate.
Fill the table with either Maximum, Minimum, or At midline:
\[\begin{array}{|c|c|c|c|c|}
P_1 & P_2 & P_3 & P_4 & P_5 \\
\hline
\hspace{10ex} & \hspace{10ex} & \hspace{10ex} & \hspace{10ex} & \hspace{10ex}
\end{array}
\]
\item
What is the unit for the graph of the function \(f(x)=5\sin(4x)-3\)?
\item
Explain how to find the \(y\)-coordinate of the
second keypoint for the graph of a transformed sine function.
\item
What is the the first key point for the graph of
\(f(t)=7\cos(2t-\pi/2)+8\)?
\item
What is the second key point for the graph of
\(f(x)=4\sin(\pi x+\pi/3)+1\)?
\end{enumerate}