Cotangent of 60 Degrees

Theorem

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

where $\cot$ denotes cotangent.

Proof

\(\ds \cot 60 \degrees\)

\(=\)

\(\ds \frac {\cos 60 \degrees} {\sin 60 \degrees}\)

Cotangent is Cosine divided by Sine

\(\ds \)

\(=\)

\(\ds \frac {\frac 1 2} {\frac {\sqrt 3} 2}\)

Cosine of $60 \degrees$ and Sine of $60 \degrees$

\(\ds \)

\(=\)

\(\ds \frac {\sqrt 3} 3\)

multiplying top and bottom by $2 \sqrt 3$

$\blacksquare$

Also presented as

Some sources present the cotangent of $60 \degrees$ as:

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

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
• 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