\chapter{Trigonometry I}
\section{The reference angle and its use}
Answer the questions.
\begin{enumerate}
\item
Explain in words what the reference angle of an angle \(\theta\) is.
\item
The reference angle for an angle \(\theta\) is \(23^\circ\). What is the reference angle for
\(\theta +180^\circ\)?
\item
Suppose \(\theta_1\) and \(\theta_2\) are co-terminal. Explain why they have the same
reference angle.
\item
Give an example of two positive angles \(\theta_1\) and \(\theta_2\) that have the same
reference angle, but are not co-terminal.
\item
Explain in words how to find the reference angle of an angle if we know its degree measure.
\item
Suppose the reference angle for \(\theta\) is \(30^\circ\), and \(\cos\theta\) is negative.
What is \(\cos \theta\)?
\item
Suppose we know that \(\theta\) is in Quadrant 4, and its reference angle is \(\displaystyle
\frac{\pi}{3}\). What is \(\tan \theta\)?
\item
We are given that \(\displaystyle \sin \theta_1 =\frac{2}{3}\). We also know that
\(\theta_2\) is in Quadrant 3, and has the same reference angle as \(\theta_1\). What is
\(\sin \theta_2\)?
\end{enumerate}