What is the value of (8sqrt(3))/3 sin(30) ?

The value of (8sqrt(3))/3 sin(30) is (4sqrt(3))/3

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(8sqrt(3))/3 sin(30)

\frac{8 3}{3} sin (3 0^{\circ})

\frac{4 3}{3}

Decimal Notation

2.30940 \dots

Solution steps

\frac{8 3}{3} sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

= \frac{8 3}{3} \cdot \frac{1}{2}

Simplify

\frac{8 3}{3} \cdot \frac{1}{2} : \frac{4 3}{3}

\frac{8 3}{3} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{8 3 \cdot 1}{3 \cdot 2}

Multiply the numbers:

8 \cdot 1 = 8

= \frac{8 3}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{8 3}{6}

Cancel the common factor:

2

= \frac{4 3}{3}

= \frac{4 3}{3}

arccos (0.607)

8 cos (1 5^{\circ})

cos (36.6 9^{\circ})

arctan (\frac{4.66}{9.8} + 0.6)

cos (1.75)

What is the value of (8sqrt(3))/3 sin(30) ?
The value of (8sqrt(3))/3 sin(30) is (4sqrt(3))/3