What is the value of sin(pi/(32)) ?

The value of sin(pi/(32)) is (sqrt(2-\sqrt{2+\sqrt{2+\sqrt{2)}}})/2

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sin(pi/(32))

sin (\frac{π}{32})

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

Solution steps

sin (\frac{π}{32})

Rewrite using trig identities:

\frac{1 - cos ( \frac{π}{16} )}{2}

= \frac{1 - cos ( \frac{π}{16} )}{2}

Rewrite using trig identities:

cos (\frac{π}{16}) = \frac{2 + 2 + 2}{2}

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

Simplify

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

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

cos (2) (30)

\frac{sin ( 7 )}{1 - sin ( 7 )}

\frac{1166}{tan ( 5 1 ^{\circ} )}

csc (- 13 0^{\circ})

3 \cdot cos (\frac{π}{4})

What is the value of sin(pi/(32)) ?
The value of sin(pi/(32)) is (sqrt(2-\sqrt{2+\sqrt{2+\sqrt{2)}}})/2