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})

Rewrite using trig identities:

sin (- \frac{2 π}{3}) = - \frac{3}{2}

sin (- \frac{2 π}{3})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{2 π}{3}) = - 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}

= 4 (- \frac{3}{2})

Simplify

4 (- \frac{3}{2}) : - 23

4 (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= - 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

arctan (tan (- \frac{2 π}{7}))

sin (2 arctan (- \frac{4}{3}))

arcsin (- \frac{π}{2})

tan (\frac{4 π}{3}) - 3

arctan (\frac{9.3}{7.5})