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Math Help - trigo problem no. 24 [general solution]

  1. #1
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    trigo problem no. 24 [general solution]

    p215 q10
    thanks
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  2. #2
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    i didn't treat cos 2x as cos ^2 x
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  3. #3
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    Quote Originally Posted by afeasfaerw23231233 View Post
    i didn't treat cos 2x as cos ^2 x
    1. Your answer of \frac{2n\pi}{3} \pm \frac{\pi}{6} is correct, the book's answer of 2n\pi + \frac{\pi}{6} misses solutions \left( \text{such as} \, \frac{5\pi}{6} \, \text{and} \, \frac{\pi}{2}\right) and so is not completely correct .....

    2. \cos^{-1} \left( \frac{-1 + \sqrt{5}}{4} \right) = \frac{2 \pi}{5} and \cos^{-1} \left( \frac{-1 - \sqrt{5}}{4} \right) = \frac{4 \pi}{5} are correct exact values. Your corresponding answers are only decimal approximations to these exact answers. But it's a bit tough to expect someone to know these exact values!!!!

    It's possible to prove that these are the exact values but it's a bit complicated.
    Last edited by mr fantastic; March 26th 2008 at 04:26 AM. Reason: Added pi/2 as another example of a solution missed by the book's answer
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    Quote Originally Posted by afeasfaerw23231233 View Post
    i didn't treat cos 2x as cos ^2 x
    I looked at the line wrong. My apologies.

    -Dan
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