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

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

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Find the Exact Value sin((2pi)/3)

sin (\frac{( 2 π )}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (\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}

sin (x) = \frac{4}{5}, cos (x) = \frac{3}{5}

\frac{50}{( tan ( 5 3 ^{\circ} ) )}

cos (\frac{( 3 π )}{2})

sin (\frac{( 3 π )}{4})

x, cos (x) = \frac{( 3 )}{2}

What is the value of sin(((2pi))/3) ?
The value of sin(((2pi))/3) is (sqrt(3))/2