Tangent of Angle minus Three Right Angles

Theorem

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


Proof

\(\ds \map \tan {x - \dfrac {3 \pi} 2}\) \(=\) \(\ds -\map \tan {x - \dfrac {\pi} 2}\) as $\map \tan {x - \dfrac {\pi} 2}$ is in the opposite quadrant to $\map \tan {x - \dfrac {3 \pi} 2}$
\(\ds \) \(=\) \(\ds \cot \theta\) Tangent of Complement equals Cotangent

$\blacksquare$


Also see


Sources

  • 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Angles larger than $90 \degrees$: Examples
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