What is the value of tan((19pi)/6) ?

The value of tan((19pi)/6) is (sqrt(3))/3

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tan((19pi)/6)

tan (\frac{19 π}{6})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

tan (\frac{19 π}{6})

tan (\frac{19 π}{6}) = tan (\frac{π}{6})

tan (\frac{19 π}{6})

Rewrite

\frac{19 π}{6}

π \cdot 3 + \frac{π}{6}

= tan (π 3 + \frac{π}{6})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 3 + \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{2 π}{4})

tan (- 13 5^{\circ})

4 cos (\frac{π}{6})

csc (- \frac{3 π}{4})

arctan (- 0.5)