Cosecant of 225 Degrees

From ProofWiki
Jump to navigation Jump to search

Theorem

$\csc 225 \degrees = \csc \dfrac {5 \pi} 4 = -\sqrt 2$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 225 \degrees\) \(=\) \(\ds \map \csc {360 \degrees - 135 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 135 \degrees\) Cosecant of Conjugate Angle
\(\ds \) \(=\) \(\ds -\sqrt 2\) Cosecant of $135 \degrees$

$\blacksquare$


Sources