Secant of 210 Degrees

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Theorem

$\sec 210 \degrees = \sec \dfrac {7 \pi} 6 = -2 \dfrac {\sqrt 3} 3$

where $\sec$ denotes secant.


Proof

\(\ds \sec 210 \degrees\) \(=\) \(\ds \map \sec {360 \degrees - 150 \degrees}\)
\(\ds \) \(=\) \(\ds \sec 150 \degrees\) Secant of Conjugate Angle
\(\ds \) \(=\) \(\ds -2 \frac {\sqrt 3} 3\) Secant of $150 \degrees$

$\blacksquare$


Sources