What is the value of tan(5/6 pi) ?

The value of tan(5/6 pi) is -(sqrt(3))/3

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tan(5/6 pi)

tan (\frac{5}{6} π)

- \frac{3}{3}

Solution steps

tan (\frac{5}{6} π)

Simplify:

\frac{5}{6} π = \frac{5 π}{6}

= tan (\frac{5 π}{6})

Rewrite using trig identities:

\frac{sin ( \frac{5 π}{6} )}{cos ( \frac{5 π}{6} )}

= \frac{sin ( \frac{5 π}{6} )}{cos ( \frac{5 π}{6} )}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

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

Simplify

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

= - \frac{3}{3}

2 sin (π) - 1

csc (\frac{22 π}{3})

10 cos (27 0^{\circ})

60 cos (4 0^{\circ})

cos (\frac{2 π}{11})