Trigonometric Functions of Three Right Angles less Angle

Theorem

Sine of Three Right Angles less Angle

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

where $\sin$ and $\cos$ are sine and cosine respectively.

Cosine of Three Right Angles less Angle

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

where $\cos$ and $\sin$ are cosine and sine respectively.

Tangent of Three Right Angles less Angle

$\tan \left({\dfrac {3 \pi} 2 - \theta}\right) = \cot \theta$

where $\tan$ and $\cot$ are tangent and cotangent respectively.

Cotangent of Three Right Angles less Angle

$\cot \left({\dfrac {3 \pi} 2 - \theta}\right) = \tan \theta$

where $\cot$ and $\tan$ are cotangent and tangent respectively.

Secant of Three Right Angles less Angle

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

where $\sec$ and $\csc$ are secant and cosecant respectively.

Cosecant of Three Right Angles less Angle

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

where $\csc$ and $\sec$ are cosecant and secant respectively.

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