Tangent of 135 Degrees

Theorem

$\tan 135^\circ = \tan \dfrac {3 \pi} 4 = - 1$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 135^\circ\) \(=\) \(\ds \tan \left({90^\circ + 45^\circ}\right)\)
\(\ds \) \(=\) \(\ds - \cot 45^\circ\) Tangent of Angle plus Right Angle
\(\ds \) \(=\) \(\ds - 1\) Cotangent of 45 Degrees

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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.