Cotangent of 60 Degrees
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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 $2 \sqrt 3$ |
$\blacksquare$
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