What is the value of 6sin((5pi)/6)cos(pi/6) ?

The value of 6sin((5pi)/6)cos(pi/6) is (3sqrt(3))/2

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6sin((5pi)/6)cos(pi/6)

6 sin (\frac{5 π}{6}) cos (\frac{π}{6})

\frac{3 3}{2}

Decimal Notation

2.59807 \dots

Solution steps

6 sin (\frac{5 π}{6}) cos (\frac{π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 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}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= 6 \cdot \frac{1}{2} \cdot \frac{3}{2}

Simplify

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

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

Multiply fractions:

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

= \frac{1 \cdot 3 \cdot 6}{2 \cdot 2}

Multiply the numbers:

1 \cdot 6 = 6

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{6 3}{4}

Cancel the common factor:

2

= \frac{3 3}{2}

= \frac{3 3}{2}

\frac{21 sin ( 8 8 ^{\circ} )}{26}

cos^{2} (2 9^{\circ})

arccos (\frac{4}{8})

30 cos (2 5^{\circ})

arctan (\frac{3.9}{2.2})

What is the value of 6sin((5pi)/6)cos(pi/6) ?
The value of 6sin((5pi)/6)cos(pi/6) is (3sqrt(3))/2