What is the value of sin((7pi)/(20)) ?

The value of sin((7pi)/(20)) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5-\sqrt{5)}})/4

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sin((7pi)/(20))

sin (\frac{7 π}{20})

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

Solution steps

sin (\frac{7 π}{20})

Rewrite using trig identities:

\frac{1 - cos ( \frac{7 π}{10} )}{2}

= \frac{1 - cos ( \frac{7 π}{10} )}{2}

Rewrite using trig identities:

cos (\frac{7 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}

tan (arccos (- \frac{5}{6}))

0.04 π cos (π \cdot 1 - π \cdot \frac{2}{6})

sin (67. 5^{\circ}) sin (22. 5^{\circ})

- 7 sin (\frac{π}{2})

csc (- 51 0^{\circ})

What is the value of sin((7pi)/(20)) ?
The value of sin((7pi)/(20)) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5-\sqrt{5)}})/4