Cosecant of 315 Degrees
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Theorem
- $\csc 315^\circ = \csc \dfrac {7 \pi} 4 = -\sqrt 2$
where $\csc$ denotes cosecant.
Proof
\(\ds \csc 315^\circ\) | \(=\) | \(\ds \csc \left({360^\circ - 45^\circ}\right)\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -\csc 45^\circ\) | Cosecant of Conjugate 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