Tangent of Angle plus Full Angle

Theorem

$\map \tan {x + 2 \pi} = \tan x$


Proof

\(\ds \map \tan {x + 2 \pi}\) \(=\) \(\ds \frac {\map \sin {x + 2 \pi} } {\map \cos {x + 2 \pi} }\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac {\sin x} {\cos x}\) Sine of Angle plus Full Angle and Cosine of Angle plus Full Angle
\(\ds \) \(=\) \(\ds \tan x\) Tangent is Sine divided by Cosine

$\blacksquare$


Also see


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
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