Definition:Secant Function/Definition from Circle/Third Quadrant

Definition
Consider a unit circle $C$ whose center is at the origin of a cartesian plane.


 * SecantThirdQuadrant.png

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.