What is the value of 48sin(30) ?

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48sin(30)

48 sin (3 0^{\circ})

24

Solution steps

48 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}

= 48 \cdot \frac{1}{2}

Simplify

48 \cdot \frac{1}{2} : 24

48 \cdot \frac{1}{2}

Convert element to fraction:

48 = \frac{48}{1}

= \frac{1}{2} \cdot \frac{48}{1}

Cross-cancel common factor:

2

= \frac{24}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 24

= 24