Cosecant of 210 Degrees

Theorem

$\csc 210 \degrees = \csc \dfrac {7 \pi} 6 = -2$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 210 \degrees\) \(=\) \(\ds \map \csc {360 \degrees - 150 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 150 \degrees\) Cosecant of Conjugate Angle
\(\ds \) \(=\) \(\ds -2\) Cosecant of $150 \degrees$

$\blacksquare$


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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