What is the value of 20*0.5sin(150) ?

The value of 20*0.5sin(150) is 5

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20*0.5sin(150)

20 \cdot 0.5 sin (15 0^{\circ})

5

Solution steps

20 \cdot 0.5 sin (15 0^{\circ})

= 20 \cdot \frac{1}{2} sin (15 0^{\circ})

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 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}

= 20 \cdot \frac{1}{2} \cdot \frac{1}{2}

Simplify

20 \cdot \frac{1}{2} \cdot \frac{1}{2} : 5

20 \cdot \frac{1}{2} \cdot \frac{1}{2}

Convert element to fraction:

20 = \frac{20}{1}

= \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{20}{1}

Multiply fractions:

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

= \frac{20 \cdot 1 \cdot 1}{1 \cdot 2 \cdot 2}

Cancel the common factor:

1

= \frac{20 \cdot 1}{2 \cdot 2}

Multiply the numbers:

20 \cdot 1 = 20

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{20}{4}

Divide the numbers:

\frac{20}{4} = 5

= 5

= 5

\frac{8}{cos ( 5 0 ^{\circ} )}

sin (400 0^{\circ}) \cdot sin (400 0^{\circ})

9 sin^{3} (3) (ln (sin (3)) + 3 cot (3))

cos (24 π)

\frac{3}{tan ( 2 6 ^{\circ} )}