What is the value of sin(-(14pi)/3) ?

The value of sin(-(14pi)/3) is -(sqrt(3))/2

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sin(-(14pi)/3)

sin (- \frac{14 π}{3})

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

sin (- \frac{14 π}{3})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{14 π}{3}) = - sin (\frac{14 π}{3})

= - sin (\frac{14 π}{3})

sin (\frac{14 π}{3}) = sin (\frac{2 π}{3})

sin (\frac{14 π}{3})

Rewrite

\frac{14 π}{3}

2 π \cdot 2 + \frac{2 π}{3}

= sin (2 π 2 + \frac{2 π}{3})

Apply the periodicity of

sin

sin (x + 2 π \cdot k) = sin (x)

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

= sin (\frac{2 π}{3})

= - sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 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}

\frac{1 + cos ( \frac{5}{13} )}{2}

sin (\frac{6 π}{7}) cos (\frac{11 π}{21}) - cos (\frac{6 π}{7}) sin (\frac{11 π}{21})

7.05 tan (4 2^{\circ})

sin^{2} (2 3^{\circ}) + sin^{2} (6 7^{\circ})

12 (4)^{5} - 12 sin (4)

What is the value of sin(-(14pi)/3) ?
The value of sin(-(14pi)/3) is -(sqrt(3))/2