Tangent of 315 Degrees

From ProofWiki
Jump to navigation Jump to search

Theorem

$\tan 315 \degrees = \tan \dfrac {7 \pi} 4 = -1$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 315 \degrees\) \(=\) \(\ds \map \tan {360 \degrees - 45 \degrees}\)
\(\ds \) \(=\) \(\ds -\tan 45 \degrees\) Tangent of Conjugate Angle
\(\ds \) \(=\) \(\ds -1\) Tangent of $45 \degrees$

$\blacksquare$


Sources