What is the value of sin(30)*3 ?

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sin(30)*3

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

\frac{3}{2}

Decimal Notation

1.5

Solution steps

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

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{1}{2} \cdot 3

Simplify

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

\frac{1}{2} \cdot 3

Convert element to fraction:

3 = \frac{3}{1}

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

Multiply fractions:

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

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

Cancel the common factor:

1

= \frac{3}{2}

= \frac{3}{2}

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