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Math Help - [SOLVED] Complex Numbers- cos ( pi/5)

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    [SOLVED] Complex Numbers- cos ( pi/5)

    I am trying to prove that cos(pi/5)= (1+sqrt(5))/4

    I tried finding the 5th roots of unity and then just using the real part cis(pi/5) but then i dont know how to get it = (1+sqrt(5))/4.
    I am stuck somewhere here.
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  3. #3
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    i am still confused though. that website is for sin(pi/5) i let x=cos(theta) and now i have (x+y)^5 and i expanded it out. but now i am still stuck.
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  4. #4
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    Cos pi/5

    Hello kayla09

    nzmathman has shown you how to find \sin \pi/5. Now use

    \cos^2(\pi/5) = 1 - \sin^2(\pi/5)

    = 1 - \frac{5-\sqrt 5}{8}

    = \frac{3+\sqrt 5}{8}

    = \frac{6+2\sqrt 5}{16}

    = \frac{1+2\sqrt 5+5}{16}

    = \frac{(1+\sqrt 5)^2}{4^2}

    \Rightarrow \cos(\pi/5) =\frac{1+\sqrt 5}{4}, taking the positive square root.

    Grandad
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    Thanks!!!
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