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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/The Trigonometric Point">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
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\section{\label{Trigonometric point}Trigonometry}

Classically, trigonometry was devoted to solving problems about triangles.
Certain functions fundamental to solving problems about triangles have
turned out to be important in many situations, even in situations that do
not involve triangles and angles.

\subsubsection{The Trigonometric Point}

The trigonometric functions are conveniently defined via another function,
the \textbf{trigonometric point}\textit{, }denoted by $P(t)$ \textit{. \ }%
You may visualize this by thinking of this as being obtained in the
following way: Let $t>0$. Take a piece of string of length $t$ and attach
one end at $(1,0)$. Wrap the string around the unit circle in the plane in
the counterclockwise direction. The other end winds up at $P(t)$. If $t<0$,
take a piece of string of length $\left| t\right| $ and wrap it around the
unit circle in the clockwise direction. The other end winds up at $P(t)$.

\begin{definition}
Let $C$ be the circle of radius $1$ with center at the origin. Let $t$ be a
real number. If $t\geq 0$, starting at the point $\left( 1,0\right) $,
measure $t$ units in the counterclockwise direction along $C$. If $t<0$,
measure $\left| t\right| $ units from $\left( 1,0\right) $ in the clockwise
direction along $C$. In either case, let $P\left( t\right) $ denote the
point. The point $P\left( t\right) =\left( x\left( t\right) ,y\left(
t\right) \right) $ is called the \textbf{trigonometric point associated with 
}$t$. The two functions $x(t)$ and $y(t)$ are called \label%
{circular functions}\textbf{circular functions}.
\end{definition}

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