What is the value of sin((3pi)/(20)) ?

The value of sin((3pi)/(20)) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4

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sin((3pi)/(20))

sin (\frac{3 π}{20})

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

Solution steps

sin (\frac{3 π}{20})

Rewrite using trig identities:

\frac{1 - cos ( \frac{3 π}{10} )}{2}

= \frac{1 - cos ( \frac{3 π}{10} )}{2}

Rewrite using trig identities:

cos (\frac{3 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}

sin (- 105 0^{\circ})

cos^{2} (\frac{4 π}{3})

tan (arcsin (\frac{3}{5}) - arccos (- 1))

\frac{( tan ( 0 ) + 1 ) - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

sin^{2} (15 0^{\circ})

What is the value of sin((3pi)/(20)) ?
The value of sin((3pi)/(20)) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5-\sqrt{5)}})/4