Trigonometric Functions of Angle plus Right Angle
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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