Secant of 315 Degrees
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Theorem
- $\sec 315 \degrees = \sec \dfrac {7 \pi} 4 = \sqrt 2$
where $\sec$ denotes secant.
Proof
\(\ds \sec 315 \degrees\) | \(=\) | \(\ds \map \sec {360 \degrees - 45 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sec 45 \degrees\) | Secant of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt 2\) | Secant 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