What is the value of tan((4pi)/6) ?

The value of tan((4pi)/6) is -sqrt(3)

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tan((4pi)/6)

tan (\frac{4 π}{6})

- 3

Solution steps

tan (\frac{4 π}{6})

Simplify:

\frac{4 π}{6} = \frac{2 π}{3}

= tan (\frac{2 π}{3})

Rewrite using trig identities:

\frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

= \frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

= \frac{\frac{3}{2}}{- \frac{1}{2}}

Simplify

\frac{\frac{3}{2}}{- \frac{1}{2}} : - 3

= - 3

arcsin (\frac{4}{5.5})

\frac{1}{2} (1 - cos (1))

arctan (\frac{- 5}{2})

arccos (0.875)

arctan (- \frac{6}{9})