What is the value of sin((31pi)/6) ?

The value of sin((31pi)/6) is -1/2

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sin((31pi)/6)

sin (\frac{31 π}{6})

- \frac{1}{2}

Solution steps

sin (\frac{31 π}{6})

sin (\frac{31 π}{6}) = sin (\frac{7 π}{6})

= sin (\frac{7 π}{6})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

= - \frac{1}{2}

arccos (\frac{2}{4})

arcsin (\frac{1}{2} - \frac{3}{5})

sin^{2} (3 π)

sin (9 2^{\circ})

arccsc (- 5)