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

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

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

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

\frac{3}{2}

Decimal Notation

1.5

Solution steps

6 sin (\frac{5 π}{6}) sin (\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:

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}

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

Simplify

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

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

Convert element to fraction:

6 = \frac{6}{1}

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

Cancel the common factor:

1

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

Multiply the numbers:

6 \cdot 1 = 6

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

= \frac{3}{2}

arccot (tan (\frac{2 π}{3}))

sin (\frac{1}{0.1})

cos (arcsin (- \frac{5}{13}))

15 0^{22} + 3 5^{2} - 2 (150) (35) cos (11 0^{\circ})

sin (2 arccos (- \frac{12}{13}))

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