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

The value of cos(pi/(10)) is (sqrt(2)sqrt(5+\sqrt{5)})/4

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cos(pi/(10))

cos (\frac{π}{10})

\frac{2 5 + 5}{4}

Solution steps

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}

100 sin (3 0^{\circ})

tan (5 π)

cos (8 5^{\circ})

20 cos (3 0^{\circ})

- sin (\frac{3 π}{4})

What is the value of cos(pi/(10)) ?
The value of cos(pi/(10)) is (sqrt(2)sqrt(5+\sqrt{5)})/4