What is the value of sin(30)*5 ?

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sin(30)*5

sin (3 0^{\circ}) \cdot 5

\frac{5}{2}

Decimal Notation

2.5

Solution steps

sin (3 0^{\circ}) \cdot 5

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 5

Simplify

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

\frac{1}{2} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{1}{2} \cdot \frac{5}{1}

Multiply fractions:

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

= \frac{1 \cdot 5}{2 \cdot 1}

Cancel the common factor:

1

= \frac{5}{2}

= \frac{5}{2}

3 cos (\frac{5 π}{4})

\frac{2 tan ( \frac{π}{10} )}{1 - tan ^{2} ( \frac{π}{10} )}

- sin (5)

- 4 cos (\frac{π}{4})

500 cos (6 0^{\circ})