What is the value of sin(2pi*1/3) ?

The value of sin(2pi*1/3) is (sqrt(3))/2

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sin(2pi*1/3)

sin (2 π \cdot \frac{1}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (2 π \frac{1}{3})

Simplify:

2 π \frac{1}{3} = \frac{2 π}{3}

2 π \frac{1}{3}

Multiply fractions:

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

= \frac{1 \cdot 2 π}{3}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 π}{3}

= sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 π}{3})

sin (x)

periodicity table with

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{3}{2}

\frac{1}{tan ( 2 5 ^{\circ} )}

cos (\frac{3 π}{33})

tan (16.2 6^{\circ})

\frac{500}{tan ( 1 5 ^{\circ} )}

cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})