Cosecant of Angle plus Three Right Angles

Theorem

$\map \csc {x + \dfrac {3 \pi} 2} = -\sec x$


Proof

\(\ds \map \csc {x + \frac {3 \pi} 2}\) \(=\) \(\ds \frac 1 {\map \sin {x + \frac {3 \pi} 2} }\) Cosecant is Reciprocal of Sine
\(\ds \) \(=\) \(\ds \frac 1 {-\cos x}\) Sine of Angle plus Three Right Angles
\(\ds \) \(=\) \(\ds -\sec x\) 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.