What is the value of sin(4 pi/3) ?

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

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sin(4 pi/3)

sin (4 \frac{π}{3})

- \frac{3}{2}

Solution steps

sin (4 \cdot \frac{π}{3})

Simplify:

4 \cdot \frac{π}{3} = \frac{4 π}{3}

= sin (\frac{4 π}{3})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= 0 \cdot \frac{1}{2} + (- 1) \frac{3}{2}

Simplify

= - \frac{3}{2}

sin (4 \frac{π}{4})

sin (103 5^{\circ})

sin^{4} (9 0^{\circ})

6 + 3 cos (0)

cos (6 0^{\circ}) + sin (6 0^{\circ})