Cotangent of 225 Degrees

Theorem

$\cot 225^\circ = \cot \dfrac {5 \pi} 4 = 1$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 225^\circ\) \(=\) \(\ds \cot \left({360^\circ - 135^\circ}\right)\)
\(\ds \) \(=\) \(\ds -\cot 135^\circ\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds 1\) Cotangent of 135 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
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