Cotangent of Three Right Angles

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Theorem

$\cot 270 \degrees = \cot \dfrac {3 \pi} 2 = 0$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 270 \degrees\) \(=\) \(\ds \map \cot {360 \degrees - 90 \degrees}\)
\(\ds \) \(=\) \(\ds -\cot 90 \degrees\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds 0\) Cotangent of Right Angle

$\blacksquare$


Also see


Sources