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

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

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tan((-7pi)/6)

tan (\frac{- 7 π}{6})

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

tan (\frac{- 7 π}{6})

Simplify

= tan (- \frac{7 π}{6})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{7 π}{6}) = - tan (\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}

cos (\frac{π}{12}) + cos (\frac{5 π}{12})

arctan (2.6)

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

cot (4 2^{\circ})

2 sin (4 5^{\circ}) cos (4 5^{\circ})