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

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

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sin(2pi-pi/3)

sin (2 π - \frac{π}{3})

- \frac{3}{2}

Solution steps

sin (2 π - \frac{π}{3})

Rewrite using trig identities:

sin (0) cos (\frac{π}{3}) - cos (0) sin (\frac{π}{3})

= sin (0) cos (\frac{π}{3}) - cos (0) sin (\frac{π}{3})

Use the following trivial identity:

sin (0) = 0

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (0) = 1

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= 0 \cdot \frac{1}{2} - 1 \cdot \frac{3}{2}

Simplify

= - \frac{3}{2}

\frac{tan ( 2 4 ^{\circ} )}{98}

csc (2 6^{\circ})

\frac{3}{sin ( 4 0 ^{\circ} )}

[6 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6}))]^{4}

32 sin (3 5^{\circ})