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Math Help - acute angle

  1. #1
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    acute angle

    find acute angle x such that

    \cos x+\cos 2x+\cos3x=-0.5
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    By writting \cos x=\frac{e^{ix}+e^{-ix}}2 you can turn the original equation into a nice one.
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  3. #3
    Senior Member JaneBennet's Avatar
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    Alternatively, note that the roots of the complex equation z^7-1=0 are

    z\ =\ 1,\ \cos{\frac{2\pi}{7}}\pm\mathrm{i}\,\sin{\frac{2\pi  }{7}},\ \cos{\frac{4\pi}{7}}\pm\mathrm{i}\,\sin{\frac{4\pi  }{7}},\ \cos{\frac{6\pi}{7}}\pm\mathrm{i}\,\sin{\frac{6\pi  }{7}}

    Sum the roots and equate to 0.
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