What is the value of sin((5pi)/3) ?

The value of sin((5pi)/3) is -(sqrt(3))/2

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sin((5pi)/3)

sin (\frac{5 π}{3})

- \frac{3}{2}

Solution steps

sin (\frac{5 π}{3})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

= - \frac{3}{2}

arccot (1)

cot (0)

sin (2 θ) = - \frac{1}{2}

2 cos^{2} (x) + cos (x) - 1 = 0, 0 \leq x < 2 π

cos (π x) = 0