Trigonometric Functions of Angle plus Three Right Angles

Theorem

Sine of Angle plus Three Right Angles

$\map \sin {x + \dfrac {3 \pi} 2} = -\cos x$

Cosine of Angle plus Three Right Angles

$\map \cos {x + \dfrac {3 \pi} 2} = \sin x$

Tangent of Angle plus Three Right Angles

$\map \tan {x + \dfrac {3 \pi} 2} = -\cot x$

Cotangent of Angle plus Three Right Angles

$\map \cot {x + \dfrac {3 \pi} 2} = -\tan x$

Secant of Angle plus Three Right Angles

$\map \sec {x + \dfrac {3 \pi} 2} = \csc x$

Cosecant of Angle plus Three Right Angles

$\map \csc {x + \dfrac {3 \pi} 2} = -\sec x$

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