What is the value of -4sin((2pi)/3) ?

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

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-4sin((2pi)/3)

- 4 sin (\frac{2 π}{3})

- 23

Decimal Notation

- 3.46410 \dots

Solution steps

- 4 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}

= - 4 \cdot \frac{3}{2}

Simplify

- 4 \cdot \frac{3}{2} : - 23

- 4 \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{3 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= - 23

= - 23

arcsin (10)

sin (0.9)

arcsin (\frac{4}{3})

- csc^{2} (\frac{5 π}{3})

arctan (\frac{30}{40})