Tangent of 150 Degrees
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Theorem
- $\tan 150 \degrees = \tan \dfrac {5 \pi} 6 = -\dfrac {\sqrt 3} 3$
where $\tan$ denotes tangent.
Proof
\(\ds \tan 150 \degrees\) | \(=\) | \(\ds \map \tan {90 \degrees + 60 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -\cot 60 \degrees\) | Tangent of Angle plus Right Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\dfrac {\sqrt 3} 3\) | Cotangent of $60 \degrees$ |
$\blacksquare$
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