What is the value of 20*sin(60)-10*(3sqrt(3))/2 ?

The value of 20*sin(60)-10*(3sqrt(3))/2 is -5sqrt(3)

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20sin(60)-10(3sqrt(3))/2

20 \cdot sin (6 0^{\circ}) - 10 \cdot \frac{3 3}{2}

- 53

Decimal

- 8.66025 \dots

Solution steps

20 sin (6 0^{\circ}) - 10 \cdot \frac{3 3}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= 20 \cdot \frac{3}{2} - 10 \cdot \frac{3 3}{2}

Simplify

20 \cdot \frac{3}{2} - 10 \cdot \frac{3 3}{2} : - 53

20 \cdot \frac{3}{2} - 10 \cdot \frac{3 3}{2}

20 \cdot \frac{3}{2} = 103

20 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 20}{2}

Divide the numbers:

\frac{20}{2} = 10

= 103

10 \cdot \frac{3 3}{2} = 153

10 \cdot \frac{3 3}{2}

Multiply fractions:

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

= \frac{3 3 \cdot 10}{2}

Multiply the numbers:

3 \cdot 10 = 30

= \frac{30 3}{2}

Divide the numbers:

\frac{30}{2} = 15

= 153

= 103 - 153

Add similar elements:

103 - 153 = - 53

= - 53

= - 53

What is the value of 20*sin(60)-10*(3sqrt(3))/2 ?
The value of 20*sin(60)-10*(3sqrt(3))/2 is -5sqrt(3)