Secant of 165 Degrees
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Theorem
- $\sec 165 \degrees = \sec \dfrac {11 \pi} {12} = -\paren {\sqrt 6 - \sqrt 2}$
where $\sec$ denotes secant.
Proof
| \(\ds \sec 165 \degrees\) | \(=\) | \(\ds \map \sec {90 \degrees + 75 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\csc 75 \degrees\) | Secant of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\paren {\sqrt 6 - \sqrt 2}\) | Cosecant of $75 \degrees$ |
$\blacksquare$
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