Cotangent of Angle plus Full Angle

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