Tangent of 60 Degrees

Theorem

$\tan 60 \degrees = \tan \dfrac \pi 3 = \sqrt 3$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 60 \degrees\) \(=\) \(\ds \frac {\sin 60 \degrees} {\cos 60 \degrees}\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac {\frac {\sqrt 3} 2} {\frac 1 2}\) Sine of $60 \degrees$ and Cosine of $60 \degrees$
\(\ds \) \(=\) \(\ds \sqrt 3\) 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
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $12$: Trigonometric formulae: Trigonometric values for some special angles
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $14$: Trigonometric formulae: Trigonometric values for some special angles
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