Secant of Angle in Cartesian Plane

Theorem

Let $P = \tuple {x, y}$ be a point in the cartesian 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:

$\sec \theta = \dfrac r x$

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

Proof

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Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: $5.11$