What is the value of sin((25pi)/(12)) ?

The value of sin((25pi)/(12)) is (sqrt(6)-sqrt(2))/4

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sin((25pi)/(12))

sin (\frac{25 π}{12})

\frac{6 - 2}{4}

Solution steps

sin (\frac{25 π}{12})

sin (\frac{25 π}{12}) = sin (\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}

arcsin (cos (\frac{π}{4}))

cos (1 3^{\circ})

12 cos (3 0^{\circ})

cos (16 0^{\circ})

cos^{2} (13 5^{\circ})

What is the value of sin((25pi)/(12)) ?
The value of sin((25pi)/(12)) is (sqrt(6)-sqrt(2))/4