\chapter{Analytic trigonometry}
\section{Trig equations I}
Answer the questions.
\begin{enumerate}
\item
Suppose that we solved an equation for \(\sin \theta\), and we found that \(\sin\theta\) is
negative. How many solutions are there in the interval \([-\pi,\pi]\)?
\item
If \(a\) is a positive number, how many solutions of the equation \(\tan x = a\) are there in
the interval \([-360^\circ,360^\circ]\)?
\item
Explain why there are no solutions of the equation \(2\sin^2 \theta+\sin \theta -6=0\).
\item
Are there any solutions of the equation \(2\tan^2 \theta+\tan \theta -6=0\)?
\item
How many solutions of the equation \(2\cos x +1=0\) are there in the interval
\([-90^\circ, 90^\circ]\)?
\item
Answer True or False:
One solution of the equation \(x^2 +x=0\) is \(x=0\). So one solution of the
equation \(\cos^2 \theta +\cos \theta =0\) is \(\theta = 0\).
\end{enumerate}