Secant of Three Right Angles

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Theorem

$\sec 270 \degrees = \sec \dfrac {3 \pi} 2$ is undefined

where $\sec$ denotes secant.


Proof

\(\ds \sec 270 \degrees\) \(=\) \(\ds \map \sec {360 \degrees - 90 \degrees}\)
\(\ds \) \(=\) \(\ds \sec 90 \degrees\) Secant of Conjugate Angle

But from Secant of Right Angle, $\sec 90 \degrees$ is undefined.

$\blacksquare$


Also see


Sources

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