What is the value of sin(5/12 pi) ?

The value of sin(5/12 pi) is (sqrt(6)+sqrt(2))/4

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sin(5/12 pi)

sin (\frac{5}{12} π)

\frac{6 + 2}{4}

Solution steps

sin (\frac{5}{12} π)

Simplify:

\frac{5}{12} π = \frac{5 π}{12}

= sin (\frac{5 π}{12})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

Simplify

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

= \frac{6 + 2}{4}

arccos (\frac{3}{4})

π - cos (π)

e^{1} cos (1)

cos (2 \cdot \frac{5 π}{6})

arcsin (tan (\frac{7 π}{4}))

What is the value of sin(5/12 pi) ?
The value of sin(5/12 pi) is (sqrt(6)+sqrt(2))/4