Cosecant of 210 Degrees

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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