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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

pi/3 sin(pi/3)

\frac{π}{3} sin (\frac{π}{3})

\frac{3 π}{6}

Decimal Notation

0.90689 \dots

Solution steps

\frac{π}{3} sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{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{π}{3} \cdot \frac{3}{2}

Simplify

\frac{π}{3} \cdot \frac{3}{2} : \frac{3 π}{6}

\frac{π}{3} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{π 3}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{3 π}{6}

= \frac{3 π}{6}

arctan (\frac{- 1}{5})

arctan (0.68)

arctan (0.63)

arctan (0.61)

\frac{19}{tan ( 3 8 ^{\circ} )}

What is the value of pi/3 sin(pi/3) ?
The value of pi/3 sin(pi/3) is (sqrt(3)pi)/6