What is the value of sin(1/12 pi) ?

The value of sin(1/12 pi) is (sqrt(6)-sqrt(2))/4

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sin(1/12 pi)

sin (\frac{1}{12} π)

\frac{6 - 2}{4}

Solution steps

sin (\frac{1}{12} π)

Simplify:

\frac{1}{12} π = \frac{π}{12}

= sin (\frac{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}

arctan (\frac{15}{9})

arccos (\frac{25}{30})

\frac{6}{tan ( 3 6 ^{\circ} )}

cos (\frac{( 2 π )}{3})

sin (arccos (0) - arccos (\frac{1}{2}))

What is the value of sin(1/12 pi) ?
The value of sin(1/12 pi) is (sqrt(6)-sqrt(2))/4