Cotangent of Right Angle

Theorem

$\cot 90 \degrees = \cot \dfrac \pi 2 = 0$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 90 \degrees\) \(=\) \(\ds \frac {\cos 90 \degrees} {\sin 90 \degrees}\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac 0 1\) Cosine of Right Angle and Sine of Right Angle
\(\ds \) \(=\) \(\ds 0\)

$\blacksquare$


Also see


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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