What is the value of sin((8pi)/6) ?

The value of sin((8pi)/6) is -(sqrt(3))/2

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sin((8pi)/6)

sin (\frac{8 π}{6})

- \frac{3}{2}

Solution steps

sin (\frac{8 π}{6})

Simplify:

\frac{8 π}{6} = \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}

- 10 arcsec (\frac{13}{10})

sin (\frac{3}{7})

sin (\frac{π}{3}) cos (\frac{π}{4}) + cos (\frac{π}{3}) sin (\frac{π}{4})

arcsin (\frac{9}{15})

sec (- \frac{11 π}{4})