What is the value of tan(1/3 pi) ?

The value of tan(1/3 pi) is square root of 3

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tan(1/3 pi)

tan (\frac{1}{3} π)

3

Decimal Notation

1.73205 \dots

Solution steps

tan (\frac{1}{3} π)

Simplify:

\frac{1}{3} π = \frac{π}{3}

\frac{1}{3} π

Multiply fractions:

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

= \frac{1 π}{3}

Multiply:

1 π = π

= \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

sin^{3} (4 5^{\circ})

400 cos (2 0^{\circ})

6 cos (\frac{4 π}{3})

\frac{7.35 \cdot sin ( 7 5 ^{\circ} )}{sin ( 3 5 ^{\circ} )}

\frac{20}{cos ( 4 5 ^{\circ} )}