What is the value of 9sin((2pi)/3) ?

The value of 9sin((2pi)/3) is (9sqrt(3))/2

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9sin((2pi)/3)

9 sin (\frac{2 π}{3})

\frac{9 3}{2}

Decimal Notation

7.79422 \dots

Solution steps

9 sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 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}

= 9 \cdot \frac{3}{2}

Simplify

9 \cdot \frac{3}{2} : \frac{9 3}{2}

9 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 9}{2}

= \frac{9 3}{2}

6 cos (π)

sin (2 arcsin (\frac{7}{25}))

tan (arctan (\frac{7}{3}))

arctan (1.1)

arcsin (\frac{3}{2}) + arccos (\frac{1}{2})