What is the value of 2sin((7pi)/3) ?

The value of 2sin((7pi)/3) is square root of 3

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2sin((7pi)/3)

2 sin (\frac{7 π}{3})

3

Decimal Notation

1.73205 \dots

Solution steps

2 sin (\frac{7 π}{3})

Rewrite using trig identities:

sin (\frac{7 π}{3}) = \frac{3}{2}

sin (\frac{7 π}{3})

sin (\frac{7 π}{3}) = sin (\frac{π}{3})

sin (\frac{7 π}{3})

Rewrite

\frac{7 π}{3}

2 π + \frac{π}{3}

= sin (2 π + \frac{π}{3})

Apply the periodicity of

sin

sin (x + 2 π) = sin (x)

sin (2 π + \frac{π}{3}) = sin (\frac{π}{3})

= sin (\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}

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

Simplify

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

2 \cdot \frac{3}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

= 3

20 sin (12 0^{\circ})

0.5 sin (0)

arcsin (sin (- \frac{6 π}{7}))

2 cos (- 3)

arcsin (- 0.46)

What is the value of 2sin((7pi)/3) ?
The value of 2sin((7pi)/3) is square root of 3