What is the value of tan((2pi)/6) ?

The value of tan((2pi)/6) is square root of 3

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tan((2pi)/6)

tan (\frac{2 π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

tan (\frac{2 π}{6})

Simplify:

\frac{2 π}{6} = \frac{π}{3}

\frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

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}

= 3

= 3

cos (4.5)

10 sin (4 8^{\circ})

tan (50 0^{\circ})

sec (\frac{25 π}{4})

cos^{2} (\frac{1}{2} arccos (- \frac{5}{13}))

What is the value of tan((2pi)/6) ?
The value of tan((2pi)/6) is square root of 3