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Math Help - 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
    :-(



    Thank you all...This is an amazing forum with amazing people.
    God bless you all.
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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 ...

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

    \sin^2{a} = 25 - 70\cos{a} + 49\cos^2{a}<br />

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

    0 = 50\cos^2{a} - 70\cos{a} + 24<br />

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

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

    \cos{a} = \frac{3}{5} ... a = \arccos\left(\frac{3}{5}\right) , a = 2\pi - \arccos\left(\frac{3}{5}\right)<br />

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

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

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