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

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

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tan((5pi)/6)

tan (\frac{( 5 π )}{6})

- \frac{3}{3}

Solution steps

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}

sin (\frac{200}{90})

x, tan (x) = 2

x, cos (2 x) = - cos (x)

sin (\frac{( 2 π )}{3})

sin (x) = \frac{4}{5}, cos (x) = \frac{3}{5}

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