Cotangent of 60 Degrees

Theorem

$\cot 60 \degrees = \cot \dfrac \pi 3 = \dfrac {\sqrt 3} 3$

where $\cot$ denotes cotangent.

$\ds \cot 60 \degrees$

$=$

$\ds \frac {\cos 60 \degrees} {\sin 60 \degrees}$

$\ds $

$=$

$\ds \frac {\frac 1 2} {\frac {\sqrt 3} 2}$

$\ds $

$=$

$\ds \frac {\sqrt 3} 3$

multiplying top and bottom by $2 \sqrt 3$

$\blacksquare$

Some sources present the as:

$\cot 60 \degrees = \cot \dfrac \pi 3 = \dfrac 1 {\sqrt 3}$

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function