Sine of Angle in Cartesian Plane

Theorem
Let $P = \left({x, y}\right)$ be a point in the cartesian coordinate plane whose origin is at $O$.

Let $\theta$ be the angle between the $x$-axis and the line $OP$.

Let $r$ be the length of $OP$.

Then:
 * $\sin \theta = \dfrac y r$

where $\sin$ denotes the sine of $\theta$.

Proof

 * SineCartesian.png

Let a unit circle $C$ be drawn with its center at the origin $O$.

Let $Q$ be the point on $OP$ which intersects $OP$.