Cotangent of Full Angle
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Theorem
- $\cot 360^\circ = \cot 2 \pi$ is undefined
where $\cot$ denotes cotangent.
Proof
From Cotangent is Cosine divided by Sine:
- $\cot \theta = \dfrac {\cos \theta} {\sin \theta}$
From Cosine of Full Angle:
- $\cos 2 \pi = 1$
From Sine of Full Angle:
- $\sin 2 \pi = 0$
Thus $\cot \theta$ is undefined at this value.
$\blacksquare$
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