\chapter{Analytic trigonometry}
\section{Trig equations II}
Answer the questions.
\begin{enumerate}
\item
Suppose that we solved an equation that involves
\(\sin \theta\) and we found that \(4\pi/3\) and \(5\pi/3\) are the solutions in the interval
\([0,2\pi]\). What are all the possible solutions of the equation, without any
interval restrictions?
\item
Suppose we need to find all the solutions of the equation \(\tan \theta= a\), where
\(a\) is a positive number. The tangent function is positive in Q1 and Q3. Is it necessary
for us to find a solution in both quadrants?
\item
When solving an equation of the form \(a\sin^2\theta+b\cos \theta +c=0\), what should
the first step be?
\item
When solving an equation such as \(\cos(2x) +a\sin x=0\), which double angle identity would you
use?
\item
Suppose we solved an equation for \(\tan\theta\) and found that the only solution
in \([0,\pi]\) is \(\pi/3\). What are all the solutions of the same equation for \(\tan(5\theta)\)?
\end{enumerate}