\chapter{Trigonometry I}
\section{The trig functions for general angles}
Answer the questions.
\begin{enumerate}
\item
How do we define the trig functions using the coordinates \((x,y)\) of a point and the distance \(r\)
from the origin?
\item
Which of the six trig functions could be undefined?
\item
Give an example of an undefined trig function.
\item
What do the letters ASTC in the sentence "All Students Take Calculus" stand for?
\item
Suppose that \(\tan \theta =2/3\) and \((x,y)\) in on the terminal side of angle \(\theta\).
Can we conclude that \(x\) is positive?
\item
Suppose that \(f(\theta)\) is one of the six trig functions that is \textbf{not} defined at all the quadrantal
angles, and \(f(0)=1\). Which function is it?
\item
Suppose \(\displaystyle \tan(\theta)=\frac{y}{x}=-\frac{5}{12}\),
and \( \displaystyle\sin(\theta)=\frac{5}{13}\).
What are \(x\) and \(y\)?
\item
From the three numbers \(x,y,r\) used to define the trig functions, we can make three pairs:
\(\{x,y\}\), \(\{x,r\}\), \(\{y,r\}\). But only one of these three pairs is enough by itself to
determine all six trig functions. Which one?
\end{enumerate}