What is the value of 6sin(2(pi/6)) ?

The value of 6sin(2(pi/6)) is 3sqrt(3)

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6sin(2(pi/6))

6 sin (2 (\frac{π}{6}))

33

Decimal Notation

5.19615 \dots

Solution steps

6 sin (2 (\frac{π}{6}))

= 6 sin (2 \cdot \frac{π}{6})

Rewrite using trig identities:

sin (2 \cdot \frac{π}{6}) = \frac{3}{2}

sin (2 \cdot \frac{π}{6})

Simplify:

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

= \frac{3}{2}

= 6 \cdot \frac{3}{2}

Simplify

6 \cdot \frac{3}{2} : 33

6 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 33

= 33

tan (15. 4^{\circ})

\frac{cot ( \frac{3 π}{2} ) - cot ( \frac{π}{6} )}{\frac{3 π}{2} - \frac{π}{6}}

tan^{2} (\frac{7 π}{4})

cos (2) + 1 - 2

3 (\frac{2 π}{3}) + 2 cos (\frac{2 π}{3})