What is the value of 3sin(pi/6) ?

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3sin(pi/6)

3 sin (\frac{π}{6})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

3 sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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}

sec (- \frac{5 π}{12})

arctan (\frac{1}{2}) + arctan (\frac{1}{3})

cos (arccos (1))

tan (1 6^{\circ})

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