Tangent of Straight Angle

Theorem

$\tan 180 \degrees = \tan \pi = 0$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 180 \degrees\) \(=\) \(\ds \frac {\sin 180 \degrees} {\cos 180 \degrees}\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac 0 {-1}\) Sine of Straight Angle and Cosine of Straight Angle
\(\ds \) \(=\) \(\ds 0\)

$\blacksquare$


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
  • 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
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