Cosecant of Three Right Angles

From ProofWiki
(Redirected from Cosecant of 270 Degrees)
Jump to navigation Jump to search

Theorem

$\csc 270 \degrees = \csc \dfrac {3 \pi} 2 = -1$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 270 \degrees\) \(=\) \(\ds \map \csc {360 \degrees - 90 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 90 \degrees\) Cosecant of Conjugate Angle
\(\ds \) \(=\) \(\ds -1\) Cosecant of Right Angle

$\blacksquare$


Also see


Sources