Cotangent of Angle plus Full Angle
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Theorem
- $\cot \left({x + 2 \pi}\right) = \cot x$
Proof
\(\ds \cot \left({x + 2 \pi}\right)\) | \(=\) | \(\ds \frac {\cos \left({x + 2 \pi}\right)} {\sin \left({x + 2 \pi}\right)}\) | Cotangent is Cosine divided by Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\cos x} {\sin x}\) | Cosine of Angle plus Full Angle and Sine of Angle plus Full Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \cot x\) | Cotangent is Cosine divided by Sine |
$\blacksquare$
Also see
- Sine of Angle plus Full Angle
- Cosine of Angle plus Full Angle
- Tangent of Angle plus Full Angle
- Secant of Angle plus Full Angle
- Cosecant of Angle plus Full Angle
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I