What is the value of sin(11/6 pi) ?

The value of sin(11/6 pi) is -1/2

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sin(11/6 pi)

sin (\frac{11}{6} π)

- \frac{1}{2}

Solution steps

sin (\frac{11}{6} π)

Simplify:

\frac{11}{6} π = \frac{11 π}{6}

= sin (\frac{11 π}{6})

Rewrite using trig identities:

sin (π) cos (\frac{5 π}{6}) + cos (π) sin (\frac{5 π}{6})

= sin (π) cos (\frac{5 π}{6}) + cos (π) sin (\frac{5 π}{6})

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

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

Simplify

= - \frac{1}{2}

arccos (\frac{4}{17})

arcsin (cot (\frac{3 π}{4}))

cos (\frac{2 π}{9})

\frac{tan ( 1 5 ^{\circ} ) + tan ( 1 5 ^{\circ} )}{1 - tan ( 1 5 ^{\circ} ) tan ( 1 5 ^{\circ} )}

arctan (\frac{- 2 3}{2})