Definition:Cosine/Definition from Circle/Second Quadrant

Definition

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

Let $P = \tuple {x, y}$ be the point on $C$ in the second 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 $AP$.

Hence in the second quadrant, the cosine is negative.

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Angles larger than $90 \degrees$