Cotangent of 225 Degrees
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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