\begin{definition}[Definition:Secant Function/Definition from Circle/Third Quadrant]
Consider a unit circle $C$ whose center is at the origin of a cartesian plane.
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Let $P$ be the point on $C$ in the third quadrant such that $\theta$ is the angle made by $OP$ with the $x$-axis.
Let a tangent line be drawn to touch $C$ at $A = \tuple {1, 0}$.
Let $OP$ be produced to meet this tangent line at $B$.
Then the '''secant''' of $\theta$ is defined as the length of $OB$.
As $OP$ needs to be produced in the opposite direction to $P$, the '''secant''' is therefore a negative number in the third quadrant.
Category:Definitions/Secant Function
\end{definition}