What is the value of 4*10*8*sin(30) ?

The value of 4*10*8*sin(30) is 160

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4108*sin(30)

4 \cdot 10 \cdot 8 \cdot sin (3 0^{\circ})

160

Solution steps

4 \cdot 10 \cdot 8 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}

= 4 \cdot 10 \cdot 8 \cdot \frac{1}{2}

Simplify

4 \cdot 10 \cdot 8 \cdot \frac{1}{2} : 160

4 \cdot 10 \cdot 8 \cdot \frac{1}{2}

Convert element to fraction:

4 = \frac{4}{1}

= 10 \cdot 8 \cdot \frac{4}{1} \cdot \frac{1}{2}

Convert element to fraction:

10 = \frac{10}{1}

= 8 \cdot \frac{4}{1} \cdot \frac{1}{2} \cdot \frac{10}{1}

Convert element to fraction:

8 = \frac{8}{1}

= \frac{4}{1} \cdot \frac{8}{1} \cdot \frac{1}{2} \cdot \frac{10}{1}

Multiply fractions:

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

= \frac{4 \cdot 10 \cdot 8 \cdot 1}{1 \cdot 1 \cdot 1 \cdot 2}

Cancel the common factor:

1

= \frac{4 \cdot 10 \cdot 8}{1 \cdot 1 \cdot 2}

Multiply the numbers:

4 \cdot 10 \cdot 8 = 320

= \frac{320}{1 \cdot 1 \cdot 2}

Multiply the numbers:

1 \cdot 1 \cdot 2 = 2

= \frac{320}{2}

Divide the numbers:

\frac{320}{2} = 160

= 160

= 160