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Math Help - Trigo question. Help needed. Need to pass up on tomorrow.

  1. #1
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    Trigo question. Help needed. Need to pass up on tomorrow.

    Given that \cos x = -\frac{2}{3} and \sin y = -\frac{1}{\sqrt 6}, that 0^\circ\le x \le360^\circ and that x and y are in the same quadrant, find, without calculator, the values of \cos\frac{x}{2}.



    Man. This question is killing me. I only get to know x and y are in quadrant 3.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by simonsong View Post
    Given that \cos x = -\frac{2}{3} and \sin y = -\frac{1}{\sqrt 6}, that 0^\circ\le x \le360^\circ and that x and y are in the same quadrant, find, without calculator, the values of \cos\frac{x}{2}.


    Man. This question is killing me. I only get to know x and y are in quadrant 3.
    \cos x=\cos \left(\frac{x}{2}+\frac{x}{2}\right)=2\cos^2\frac{  x}{2}-1 hence \cos \frac{x}{2}=\ldots

    This should give you two values for \cos \frac{x}{2}. As you also know in which quadrant is \frac{x}{2}, you can choose the right solution among the two you've found.
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  3. #3
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    Omg. Never thought of that. Haha. Really thanks pal.
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