Tangent of Zero

Theorem

$\tan 0 = 0$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 0\) \(=\) \(\ds \frac {\sin 0} {\cos 0}\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac 0 1\) Sine of Zero is Zero and Cosine of Zero is One
\(\ds \) \(=\) \(\ds 0\)

$\blacksquare$


Also see


Sources

  • 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
  • 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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