Cosecant of 120 Degrees
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Theorem
- $\csc 120 \degrees = \csc \dfrac {2 \pi} 3 = \dfrac {2 \sqrt 3} 3$
where $\csc$ denotes cosecant.
Proof
| \(\ds \csc 120 \degrees\) | \(=\) | \(\ds \map \csc {180 \degrees - 60 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \csc 60 \degrees\) | Cosecant of Supplementary Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {2 \sqrt 3} 3\) | 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