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