\chapter{Analytic trigonometry}
\section{The basic trig identities}
Answer True or False:
\begin{enumerate}
\item
The algebra needed to simplify trigonometric expressions is different and harder than usual.
\item
If \(f\) is one of the six trigonometric functions and we know \(f(\theta)\), then
we can also find what \(f(-\theta)\) is.
\item
\(\sec \theta \cos \theta =1\), no matter what \(\theta \) is.
\item
\(\tan \theta \cot \theta\) is \(1\) for every acute angle \(\theta\).
\item
It could happen that \(\sin \theta \) is positive, but \(\cos(90^\circ -\theta)\) is negative.
\item
If we know what \(\sin^2 \theta\) is, then we also know what \(\cos \theta\) is.
\item
If we know what \(\sin^2 \theta\) is, then we also know what \(\cos^2 \theta\) is.
\item
To rationalize \(\sqrt{9-x^2}\), both \(x=3\sin \theta\) and \(x=3\cos \theta\) will work.
\item
\(\sqrt{4-x^2}\) can be rationalized with a trig substitution, but \(\sqrt{x^2-4}\) cannot.
\end{enumerate}