Cotangent of Three Right Angles less Angle

Theorem

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

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


Proof

\(\ds \cot \left({\frac {3 \pi} 2 - \theta}\right)\) \(=\) \(\ds \frac {\cos \left({\frac {3 \pi} 2 - \theta}\right)} {\sin \left({\frac {3 \pi} 2 - \theta}\right)}\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {-\sin \theta} {-\cos \theta}\) Cosine of Three Right Angles and Sine of Three Right Angles
\(\ds \) \(=\) \(\ds \tan \theta\) Tangent is Sine divided by Cosine

$\blacksquare$


Also see


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
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