What is the value of 8sin(pi/6)cos(pi/3) ?

The value of 8sin(pi/6)cos(pi/3) is 2

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8sin(pi/6)cos(pi/3)

8 sin (\frac{π}{6}) cos (\frac{π}{3})

2

Solution steps

8 sin (\frac{π}{6}) cos (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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{1}{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}

= 8 \cdot \frac{1}{2} \cdot \frac{1}{2}

Simplify

8 \cdot \frac{1}{2} \cdot \frac{1}{2} : 2

8 \cdot \frac{1}{2} \cdot \frac{1}{2}

Convert element to fraction:

8 = \frac{8}{1}

= \frac{8}{1} \cdot \frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{8 \cdot 1 \cdot 1}{1 \cdot 2 \cdot 2}

Cancel the common factor:

1

= \frac{8 \cdot 1}{2 \cdot 2}

Multiply the numbers:

8 \cdot 1 = 8

= \frac{8}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{8}{4}

Divide the numbers:

\frac{8}{4} = 2

= 2

= 2

cos (ln (2))

sin (- 25 5^{\circ})

sin (5 \cdot \frac{π}{2})

arccos (\frac{2.9}{3.2})

600 cos (4 0^{\circ})

What is the value of 8sin(pi/6)cos(pi/3) ?
The value of 8sin(pi/6)cos(pi/3) is 2