Secant of Angle plus Straight Angle

Theorem

$\map \sec {x + \pi} = -\sec x$


Proof

\(\ds \map \sec {x + \pi}\) \(=\) \(\ds \frac 1 {\map \cos {x + \pi} }\) Secant is Reciprocal of Cosine
\(\ds \) \(=\) \(\ds \frac 1 {-\cos x}\) Cosine of Angle plus Straight Angle
\(\ds \) \(=\) \(\ds -\sec x\) Secant is Reciprocal of Cosine

$\blacksquare$


Also see


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.