What is the value of tan(4/3 pi) ?

The value of tan(4/3 pi) is square root of 3

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tan(4/3 pi)

tan (\frac{4}{3} π)

3

Decimal Notation

1.73205 \dots

Solution steps

tan (\frac{4}{3} π)

Simplify:

\frac{4}{3} π = \frac{4 π}{3}

\frac{4}{3} π

Multiply fractions:

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

= \frac{4 π}{3}

= tan (\frac{4 π}{3})

tan (\frac{4 π}{3}) = tan (\frac{π}{3})

tan (\frac{4 π}{3})

Rewrite

\frac{4 π}{3}

π + \frac{π}{3}

= tan (π + \frac{π}{3})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{3}) = tan (\frac{π}{3})

= tan (\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^{2} (3 6^{\circ})

cos (10 4^{\circ})

sec (8 3^{\circ})

sec (2 arctan (\frac{4}{3}))

1 - sin (\frac{2 π}{3})