Cotangent of 30 Degrees
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Theorem
- $\cot 30 \degrees = \cot \dfrac \pi 6 = \sqrt 3$
where $\cot$ denotes cotangent.
Proof
\(\ds \cot 30 \degrees\) | \(=\) | \(\ds \frac {\cos 30 \degrees} {\sin 30 \degrees}\) | Cotangent is Cosine divided by Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\frac {\sqrt 3} 2} {\frac 1 2}\) | Cosine of $30 \degrees$ and Sine of $30 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt 3\) | multiplying top and bottom by $2$ |
$\blacksquare$
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