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