Cotangent of Full Angle

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
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