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Thread: 2 questions

  1. #1
    Newbie
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    2 questions

    Hi...
    I am so sorry for posting so many question but i have an exam soon, and there are some questions that might appear in the exam and i don't know how to solve them
    :-(



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  2. #2
    MHF Contributor
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    Quote Originally Posted by rectangle View Post
    Hi...


    you didn't pick the easy ones ...

    $\displaystyle \sin{a} = 5 - 7\cos{a}$

    $\displaystyle \sin^2{a} = 25 - 70\cos{a} + 49\cos^2{a}
    $

    $\displaystyle 1 - \cos^2{a} = 25 - 70\cos{a} + 49\cos^2{a}$

    $\displaystyle 0 = 50\cos^2{a} - 70\cos{a} + 24
    $

    $\displaystyle 0 = 2(5\cos{a}-4)(5\cos{a}-3}$

    $\displaystyle \cos{a} = \frac{4}{5}$ ... $\displaystyle a = \arccos\left(\frac{4}{5}\right)$ , $\displaystyle a = 2\pi - \arccos\left(\frac{4}{5}\right)$

    $\displaystyle \cos{a} = \frac{3}{5}$ ... $\displaystyle a = \arccos\left(\frac{3}{5}\right)$ , $\displaystyle a = 2\pi - \arccos\left(\frac{3}{5}\right)
    $

    note that the above solutions are in the interval $\displaystyle [0,2\pi]$

    -------------------------

    I'll have to mull over the 2nd problem if I get the time.
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