Trigonometric Functions of Angle plus Straight Angle

Theorem

Sine of Angle plus Straight Angle

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


Cosine of Angle plus Straight Angle

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


Tangent of Angle plus Straight Angle

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


Cotangent of Angle plus Straight Angle

$\map \cot {x + \pi} = \cot x$


Secant of Angle plus Straight Angle

$\map \sec {x + \pi} = -\sec x$


Cosecant of Angle plus Straight Angle

$\map \csc {x + \pi} = -\csc x$


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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