What is the value of sin((23pi)/(12)) ?

The value of sin((23pi)/(12)) is (sqrt(2)-sqrt(6))/4

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sin((23pi)/(12))

sin (\frac{23 π}{12})

\frac{2 - 6}{4}

Solution steps

sin (\frac{23 π}{12})

Rewrite using trig identities:

sin (\frac{5 π}{4}) cos (\frac{2 π}{3}) + cos (\frac{5 π}{4}) sin (\frac{2 π}{3})

= sin (\frac{5 π}{4}) cos (\frac{2 π}{3}) + cos (\frac{5 π}{4}) sin (\frac{2 π}{3})

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

(- \frac{2}{2}) (- \frac{1}{2}) + (- \frac{2}{2}) \frac{3}{2} : \frac{2 - 6}{4}

= \frac{2 - 6}{4}

- csc^{2} (6 0^{\circ})

cos (5 2^{\circ})

cos (\frac{- π}{4})

arccos (0.75)

cos^{2} (\frac{3 π}{4})

What is the value of sin((23pi)/(12)) ?
The value of sin((23pi)/(12)) is (sqrt(2)-sqrt(6))/4