What is the value of sin((9pi)/(10)) ?

The value of sin((9pi)/(10)) is (sqrt(2)sqrt(3-\sqrt{5)})/4

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sin((9pi)/(10))

sin (\frac{9 π}{10})

\frac{2 3 - 5}{4}

Solution steps

sin (\frac{9 π}{10})

Rewrite using trig identities:

sin (\frac{π}{10})

= sin (\frac{π}{10})

Rewrite using trig identities:

\frac{1 - cos ( \frac{π}{5} )}{2}

= \frac{1 - cos ( \frac{π}{5} )}{2}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

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

Simplify

\frac{1 - \frac{5 + 1}{4}}{2} : \frac{2 3 - 5}{4}

= \frac{2 3 - 5}{4}

150 cos (1 5^{\circ})

arctan (\frac{6}{2})

tan (arcsin (\frac{7}{9}))

- 8 sin (\frac{π}{4})

2 sin (1 0^{\circ})

What is the value of sin((9pi)/(10)) ?
The value of sin((9pi)/(10)) is (sqrt(2)sqrt(3-\sqrt{5)})/4