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
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles