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