What is the value of sin((7pi)/(16)) ?

The value of sin((7pi)/(16)) is (sqrt(2+\sqrt{2+\sqrt{2)}})/2

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sin((7pi)/(16))

sin (\frac{7 π}{16})

\frac{2 + 2 + 2}{2}

Solution steps

sin (\frac{7 π}{16})

Rewrite using trig identities:

\frac{1 - cos ( \frac{7 π}{8} )}{2}

= \frac{1 - cos ( \frac{7 π}{8} )}{2}

Rewrite using trig identities:

cos (\frac{7 π}{8}) = - \frac{2 + 2}{2}

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

Simplify

\frac{1 - ( - \frac{2 + 2}{2} )}{2} : \frac{2 + 2 + 2}{2}

= \frac{2 + 2 + 2}{2}

2 cos (- \frac{π}{4}) + \frac{π}{4}

sin (- 8 π)

sin (\frac{π}{2} + 1)

cos (\frac{3 π}{5}) cos (\frac{7 π}{30}) - sin (\frac{3 π}{5}) sin (\frac{7 π}{30})

- \frac{1}{4} csc (2 (- \frac{π}{2})^{2})

What is the value of sin((7pi)/(16)) ?
The value of sin((7pi)/(16)) is (sqrt(2+\sqrt{2+\sqrt{2)}})/2