Trigonometric Functions of Angle plus Right Angle

Theorem

Sine of Angle plus Right Angle

$\sin \paren {x + \dfrac \pi 2} = \cos x$

Cosine of Angle plus Right Angle

$\map \cos {x + \dfrac \pi 2} = -\sin x$

Tangent of Angle plus Right Angle

$\map \tan {x + \dfrac \pi 2} = -\cot x$

Cotangent of Angle plus Right Angle

$\map \cot {x + \dfrac \pi 2} = -\tan x$

Secant of Angle plus Right Angle

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

Cosecant of Angle plus Right Angle

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

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