Tangent of Angle plus Full Angle
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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
- Sine of Angle plus Full Angle
- Cosine of Angle plus Full Angle
- Cotangent 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