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

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

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tan(((4pi)/3)/(4))

tan (\frac{\frac{4 π}{3}}{4})

3

Decimal Notation

1.73205 \dots

Solution steps

tan (\frac{\frac{4 π}{3}}{4})

Simplify:

\frac{\frac{4 π}{3}}{4} = \frac{π}{3}

\frac{\frac{4 π}{3}}{4}

Apply the fraction rule:

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

= \frac{4 π}{3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{4 π}{12}

Cancel the common factor:

4

= \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

160 sin (6 0^{\circ})

- sin (\frac{13 π}{12})

110.7 \cdot cos (1 2^{\circ})

2 sin (4 9^{\circ})

arccos (\frac{4}{32})

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