What is the value of cos((2pi)/5) ?

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

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cos((2pi)/5)

cos (\frac{2 π}{5})

\frac{2 3 - 5}{4}

Solution steps

cos (\frac{2 π}{5})

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}

cos (\frac{- π}{3})

cos (- \frac{5 π}{3})

4 cos (0)

10 cos (3 0^{\circ})

sin (arccos (\frac{3}{5}))

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