Tangent of Straight Angle
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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
- Sine of Straight Angle
- Cosine of Straight Angle
- Cotangent of Straight Angle
- Secant of Straight Angle
- Cosecant of Straight Angle
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