What is the value of 4*0.11*sin(30) ?

The value of 4*0.11*sin(30) is 11/50

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40.11sin(30)

4 \cdot 0.11 \cdot sin (3 0^{\circ})

\frac{11}{50}

Decimal Notation

0.22

Solution steps

4 \cdot 0.11 sin (3 0^{\circ})

= 4 \cdot \frac{11}{100} 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 \frac{11}{100} \cdot \frac{1}{2}

Simplify

4 \cdot \frac{11}{100} \cdot \frac{1}{2} : \frac{11}{50}

4 \cdot \frac{11}{100} \cdot \frac{1}{2}

Convert element to fraction:

4 = \frac{4}{1}

= \frac{4}{1} \cdot \frac{1}{2} \cdot \frac{11}{100}

Multiply fractions:

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

= \frac{4 \cdot 11 \cdot 1}{1 \cdot 100 \cdot 2}

Cancel the common factor:

1

= \frac{4 \cdot 11}{100 \cdot 2}

Multiply the numbers:

4 \cdot 11 = 44

= \frac{44}{100 \cdot 2}

Multiply the numbers:

100 \cdot 2 = 200

= \frac{44}{200}

Cancel the common factor:

4

= \frac{11}{50}

= \frac{11}{50}

\frac{sin ( 1 6 ^{\circ} )}{1 + cos ( 1 6 ^{\circ} )}

sin (49.9 6^{\circ})

2 cos (\frac{5 π}{6}) + sin (2 (\frac{5 π}{6}))

\frac{1 - cos ( 3 ( 0.999 ) - 3 )}{5 ( ( 0.999 ) - 1 ) ^{2}}

sin (6 0^{\circ}) - sin (3 0^{\circ})