What is the value of sin(19/12 pi) ?

The value of sin(19/12 pi) is (sqrt(2)(-1-sqrt(3)))/4

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sin(19/12 pi)

sin (\frac{19}{12} π)

\frac{2 ( - 1 - 3 )}{4}

Solution steps

sin (\frac{19}{12} π)

Simplify:

\frac{19}{12} π = \frac{19 π}{12}

= sin (\frac{19 π}{12})

Rewrite using trig identities:

sin (\frac{5 π}{6}) cos (\frac{3 π}{4}) + cos (\frac{5 π}{6}) sin (\frac{3 π}{4})

= sin (\frac{5 π}{6}) cos (\frac{3 π}{4}) + cos (\frac{5 π}{6}) sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

\frac{1}{2} (- \frac{2}{2}) + (- \frac{3}{2}) \frac{2}{2} : \frac{2 ( - 1 - 3 )}{4}

= \frac{2 ( - 1 - 3 )}{4}

arccos (\frac{2.3}{2.8})

sec (\frac{π}{7})

\frac{1}{tan ( 4 5 ^{\circ} )}

cot (\frac{11 π}{2})

sec (5 9^{\circ})

What is the value of sin(19/12 pi) ?
The value of sin(19/12 pi) is (sqrt(2)(-1-sqrt(3)))/4