Tangent of Full Angle
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Theorem
- $\tan 360^\circ = \tan 2 \pi = 0$
where $\tan$ denotes tangent.
Proof
| \(\ds \tan 360^\circ\) | \(=\) | \(\ds \tan \left({360^\circ - 0^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 0\) | Tangent of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds 0\) | Tangent of Zero |
$\blacksquare$
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