What is the value of 4sin(2(pi/6)) ?

The value of 4sin(2(pi/6)) is 2sqrt(3)

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4sin(2(pi/6))

4 sin (2 (\frac{π}{6}))

23

Decimal Notation

3.46410 \dots

Solution steps

4 sin (2 (\frac{π}{6}))

= 4 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}

= 4 \cdot \frac{3}{2}

Simplify

4 \cdot \frac{3}{2} : 23

4 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 23

= 23

arcsin (\frac{sin ( 6 0 ^{\circ} )}{1.5})

sin (\frac{5 π}{36})

sin (2 (4 5^{\circ}))

arctan (0.03)

cos^{2} (0) + cos (0)