What is the value of sin(pi/(20)) ?

The value of sin(pi/(20)) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5+\sqrt{5)}})/4

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sin(pi/(20))

sin (\frac{π}{20})

\frac{2 4 - 2 5 + 5}{4}

Solution steps

sin (\frac{π}{20})

Rewrite using trig identities:

\frac{1 - cos ( \frac{π}{10} )}{2}

= \frac{1 - cos ( \frac{π}{10} )}{2}

Rewrite using trig identities:

cos (\frac{π}{10}) = \frac{2 5 + 5}{4}

= \frac{1 - \frac{2 5 + 5}{4}}{2}

Simplify

\frac{1 - \frac{2 5 + 5}{4}}{2} : \frac{2 4 - 2 5 + 5}{4}

= \frac{2 4 - 2 5 + 5}{4}

cos (\frac{π}{3} - \frac{π}{4})

cos (arctan (\frac{24}{7}))

- 2 cos (- \frac{π}{3})

sin (100 0^{\circ})

tan (\frac{1}{4} π)

What is the value of sin(pi/(20)) ?
The value of sin(pi/(20)) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5+\sqrt{5)}})/4