Secant of Straight Angle

Theorem

$\sec 180 \degrees = \sec \pi = -1$

where $\sec$ denotes secant.


Proof

\(\ds \sec 180 \degrees\) \(=\) \(\ds \map \sec {90 \degrees + 90 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 90 \degrees\) Secant of Angle plus Right Angle
\(\ds \) \(=\) \(\ds -1\) Cosecant of Right Angle

$\blacksquare$


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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