Cosecant of Angle in Cartesian Plane

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Theorem

Let $P = \tuple {x, y}$ 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:

$\csc \theta = \dfrac r x$

where $\csc$ denotes the secant of $\theta$.


Proof


Sources