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

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

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sin(pi/(10))

sin (\frac{π}{10})

\frac{2 3 - 5}{4}

Solution steps

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}

sin (\frac{13 π}{4})

6 cos (\frac{π}{4})

sin (\frac{1}{0})

cot (2 5^{\circ})

cot (3 5^{\circ})

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