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