Secant of 150 Degrees

Theorem

$\sec 150 \degrees = \sec \dfrac {5 \pi} 6 = -\dfrac {2 \sqrt 3} 3$

where $\sec$ denotes secant.


Proof

\(\ds \sec 150 \degrees\) \(=\) \(\ds \map \sec {90 \degrees + 60 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 60 \degrees\) Secant of Angle plus Right Angle
\(\ds \) \(=\) \(\ds -\dfrac {2 \sqrt 3} 3\) Cosecant of $60 \degrees$

$\blacksquare$


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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