Secant of 345 Degrees
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Theorem
- $\sec 345 \degrees = \sec \dfrac {23 \pi} {12} = \sqrt 6 - \sqrt 2$
where $\sec$ denotes secant.
Proof
| \(\ds \sec 345 \degrees\) | \(=\) | \(\ds \map \sec {360 \degrees - 15 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sec 15 \degrees\) | Secant of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sqrt 6 - \sqrt 2\) | Secant of $15 \degrees$ |
$\blacksquare$
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