What is the value of -6sin((2pi)/3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-6sin((2pi)/3)

- 6 sin (\frac{2 π}{3})

- 33

Decimal Notation

- 5.19615 \dots

Solution steps

- 6 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}

= - 6 \cdot \frac{3}{2}

Simplify

- 6 \cdot \frac{3}{2} : - 33

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

Multiply fractions:

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

= - \frac{3 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= - 33

= - 33

\frac{53 sin ( 6 )}{sin ( 11 6 ^{\circ} )}

π + arctan (\frac{1}{3})

- sin (\frac{2 π}{4})

32.09 (1 + 0.0053 sin^{2} (4 5^{\circ}))

arctan (tan (- \frac{π}{7}))