What is the value of tan(7/6 pi) ?

The value of tan(7/6 pi) is (sqrt(3))/3

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tan(7/6 pi)

tan (\frac{7}{6} π)

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

tan (\frac{7}{6} π)

Simplify:

\frac{7}{6} π = \frac{7 π}{6}

\frac{7}{6} π

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 π}{6}

= tan (\frac{7 π}{6})

tan (\frac{7 π}{6}) = tan (\frac{π}{6})

tan (\frac{7 π}{6})

Rewrite

\frac{7 π}{6}

π + \frac{π}{6}

= tan (π + \frac{π}{6})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{6}) = tan (\frac{π}{6})

= tan (\frac{π}{6})

= tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

arctan (\frac{- 2}{- 2 3})

2 sin (\frac{π}{12})

22 arctan (\frac{2}{2}) + ln (3) - 2

tan (3 5^{\circ}) sec (5 5^{\circ}) cos (3 5^{\circ})

\frac{1 - cos ( 22 5 ^{\circ} )}{2}