Trigonometric Functions of Three Right Angles less Angle
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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