Secant of 255 Degrees
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Theorem
- $\sec 255 \degrees = \sec \dfrac {17 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$
where $\sec$ denotes secant.
Proof
\(\ds \sec 255 \degrees\) | \(=\) | \(\ds \map \sec {360 \degrees - 105 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sec 105 \degrees\) | Secant of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\paren {\sqrt 6 + \sqrt 2}\) | Secant of $105 \degrees$ |
$\blacksquare$
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