Secant of Right Angle

Theorem

$\sec 90 \degrees = \sec \dfrac \pi 2$ is undefined

where $\sec$ denotes secant.


Proof

From Secant is Reciprocal of Cosine:

$\sec \theta = \dfrac 1 {\cos \theta}$

From Cosine of Right Angle:

$\cos \dfrac \pi 2 = 0$

Thus $\sec \theta$ is undefined at this value.

$\blacksquare$


Also see


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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