What is the value of 3sin(30) ?

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3sin(30)

3 sin (3 0^{\circ})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

3 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}

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

Simplify

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

3 \cdot \frac{1}{2}

Convert element to fraction:

3 = \frac{3}{1}

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

Multiply fractions:

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

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

Cancel the common factor:

1

= \frac{3}{2}

= \frac{3}{2}

arccos (- \frac{2}{3})

sin (arccos (\frac{3}{2}))

2 cos^{2} (1 5^{\circ}) - 1

2 sin (6 0^{\circ})

arctan (tan (\frac{10 π}{11}))