What is the value of sin(4*pi/6) ?

The value of sin(4*pi/6) is (sqrt(3))/2

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sin(4*pi/6)

sin (4 \cdot \frac{π}{6})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (4 \cdot \frac{π}{6})

Simplify:

4 \cdot \frac{π}{6} = \frac{2 π}{3}

4 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 4}{6}

Cancel the common factor:

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{3 cos ( 0.5 ( 21 ) )}{e ^{(- 0.1 (21))}}

\frac{3}{tan ( 22. 5 ^{\circ} )}

- \frac{1}{2} sin (18 0^{\circ})

cos (61 1^{\circ})

arctan (tan (9.8488500000000 \dots))