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