Cosecant of 135 Degrees

Theorem

$\csc 135 \degrees = \csc \dfrac {3 \pi} 4 = \sqrt 2$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 135 \degrees\) \(=\) \(\ds \map \csc {180 \degrees - 45 \degrees}\)
\(\ds \) \(=\) \(\ds \csc 45 \degrees\) Cosecant of Supplementary Angle
\(\ds \) \(=\) \(\ds \sqrt 2\) Cosecant of $45 \degrees$

$\blacksquare$


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
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