Trigonometric Functions of Angle plus Full Angle

Theorem

Sine of Angle plus Full Angle

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


Cosine of Angle plus Full Angle

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


Tangent of Angle plus Full Angle

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


Cotangent of Angle plus Full Angle

$\cot \left({x + 2 \pi}\right) = \cot x$


Secant of Angle plus Full Angle

$\sec \left({x + 2 \pi}\right) = \sec x$


Cosecant of Angle plus Full Angle

$\csc \left({x + 2 \pi}\right) = \csc x$


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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