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    (d) Hence find the exact values of  \tan \left (\frac{k}{16} \pi \right ) for  k=1,5,9 \text{ and } 16 .
    Any ideas for part d?
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    (Original post by Ano123)
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    (d) Hence find the exact values of  \tan \left (\frac{k}{16} \pi \right ) for  k=1,5,9 \text{ and } 16 .
    Any ideas for part d?
    Solve the quartic given in the question.
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    How do you suppose I do that? It won't factorise nicely.
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    If you let t=\tan(\theta) then you get the quartic when \tan(4\theta)=1.

    So find the solutions of that.

    For d) Find what the sum of the squares of the roots is. Use \Sigma \alpha^2 = (\Sigma \alpha)^2 - 2\Sigma \alpha \beta

    You might also need to convert some of the roots from c) so you answer d)

    Hope that helps
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    (Original post by Math12345)
    If you let t=\tan(\theta) then you get the quartic when \tan(4\theta)=1.

    So find the solutions of that.

    For d) Find what the sum of the squares of the roots is. Use \Sigma \alpha^2 = (\Sigma \alpha)^2 - 2\Sigma \alpha \beta

    You might also need to convert some of the roots from c) so you answer d)

    Hope that helps
    It's only part d that is the trouble.
 
 
 
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