What is the value of tan(11/6 pi) ?

The value of tan(11/6 pi) is -(sqrt(3))/3

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tan(11/6 pi)

tan (\frac{11}{6} π)

- \frac{3}{3}

Solution steps

tan (\frac{11}{6} π)

Simplify:

\frac{11}{6} π = \frac{11 π}{6}

= tan (\frac{11 π}{6})

tan (\frac{11 π}{6}) = tan (\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}

\frac{14}{cos ( 4 9 ^{\circ} )}

15 \cdot cos (3 5^{\circ})

\frac{20}{cos ( 3 0 ^{\circ} )}

7 sin (π)

arcsin (- \frac{5}{6})