What is the value of sin(13/12 pi) ?

The value of sin(13/12 pi) is (sqrt(2)(1-sqrt(3)))/4

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sin(13/12 pi)

sin (\frac{13}{12} π)

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

Solution steps

sin (\frac{13}{12} π)

Simplify:

\frac{13}{12} π = \frac{13 π}{12}

= sin (\frac{13 π}{12})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{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{π}{4}) = \frac{2}{2}

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

Simplify

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

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

22 cos (4 5^{\circ})

sinh^{2} (1)

arcsin (- 0.34)

arctan (2) - arctan (1)

cot (arccos (- \frac{3}{4}))

What is the value of sin(13/12 pi) ?
The value of sin(13/12 pi) is (sqrt(2)(1-sqrt(3)))/4