Cosecant of 195 Degrees
Theorem
- $\csc 195^\circ = \csc \dfrac {13 \pi} {12} = - \left({\sqrt 6 + \sqrt 2}\right)$
where $\csc$ denotes cosecant.
Proof
| \(\ds \csc 195^\circ\) | \(=\) | \(\ds \csc \left({360^\circ - 165^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\csc 165^\circ\) | Cosecant of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds - \left({\sqrt 6 + \sqrt 2}\right)\) | Cosecant of 165 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