Definition:Cosine/Definition from Circle/Third Quadrant

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


 * CosineThirdQuadrant.png

Let $P = \tuple {x, y}$ be the point on $C$ in the third quadrant such that $\theta$ is the angle made by $OP$ with the $x$-axis.

Let $AP$ be the perpendicular from $P$ to the $y$-axis.

Then the cosine of $\theta$ is defined as the length of $AP$.

Thus by definition of third quadrant, the cosine of such an angle is negative.