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Math Help - Those double angle formulas >.<!

  1. #1
    Senior Member sakonpure6's Avatar
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    Those double angle formulas >.<!

    I have been stuck on a question for the past 40 minutes, it seems really simple. But, I can not get the right answer. Please help me, I don't like the feeling of an unsolved question!!!
    The angle x lies in the interval pi/2 <=x<=pi, and sin^2x = 8/9 . Without using a calculator, determine the value of cos x/2.
    I tried solutions like this:

    cos x/2 = cos 2(x/4) = 1-2sin^2(x/4) // What now? This is wrong right?
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  2. #2
    MHF Contributor
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    Re: Those double angle formulas >.<!

    Why are you bringing in angles of \displaystyle \begin{align*} \frac{x}{4} \end{align*} when your question clearly has angles of \displaystyle \begin{align*} x \end{align*}?

    You should be doing

    \displaystyle \begin{align*} \cos{(2\theta)} &= 2\cos{(\theta)} - 1 \\ \cos{(x)} &= 2\cos{ \left( \frac{x}{2} \right) } - 1 \end{align*}

    if we have \displaystyle \begin{align*} x = \frac{\theta}{2} \end{align*}.
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  3. #3
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    Re: Those double angle formulas >.<!

    I started by finding what sinx= and what cosx= (from a triangle and a knowledge of signs)
    and then I used the same information as Proove It did.
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