What is the value of sin((3pi)/5) ?

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

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sin((3pi)/5)

sin (\frac{3 π}{5})

\frac{2 5 + 5}{4}

Solution steps

sin (\frac{3 π}{5})

Rewrite using trig identities:

cos (\frac{π}{10})

= cos (\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 5 + 5}{4}

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

sin (- 31 5^{\circ})

cot (- 4 5^{\circ})

cos (arccos (- \frac{1}{2}))

sin (0.01)

sec^{2} (3 0^{\circ})

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