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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(pi/3)cos(pi/3)

sin (\frac{π}{3}) cos (\frac{π}{3})

\frac{3}{4}

Decimal Notation

0.43301 \dots

Solution steps

sin (\frac{π}{3}) cos (\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}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{3}{2} \cdot \frac{1}{2}

Simplify

\frac{3}{2} \cdot \frac{1}{2} : \frac{3}{4}

\frac{3}{2} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{3 \cdot 1}{2 \cdot 2}

Multiply:

3 \cdot 1 = 3

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3}{4}

= \frac{3}{4}

\frac{574 - 67 \cdot 9.8 \cdot ( sin ( 3 9 ^{\circ} ) + 0.39 \cdot cos ( 3 9 ^{\circ} ) )}{67}

arctan (tan (\frac{6 π}{5}))

sin (2 0^{\circ}) cos (3 0^{\circ}) - cos (2 0^{\circ}) sin (3 0^{\circ})

sec (arcsin (- \frac{3}{5}))

sin (- 157.3 8^{\circ})

What is the value of sin(pi/3)cos(pi/3) ?
The value of sin(pi/3)cos(pi/3) is (sqrt(3))/4