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Math Help - Question on trigonometric equations?

  1. #1
    Super Member fardeen_gen's Avatar
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    Question on trigonometric equations?

    Find all the angles θ between -π to π that satisfy the equation 5 cos 2θ + 2 cos^2 θ/2 + 1 = 0?

    The given answer includes + or - π/6, π - cos^-1 3/5 and -π + cos ^-1 3/5.

    My own answers are not matching. Please help!
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by fardeen_gen View Post
    Find all the angles θ between -π to π that satisfy the equation 5 cos 2θ + 2 cos^2 θ/2 + 1 = 0?

    The given answer includes + or - π/6, π - cos^-1 3/5 and -π + cos ^-1 3/5.

    My own answers are not matching. Please help!
    \cos 2t=2 \cos^2t-1

    --> \cos \theta=2 \cos^2 \frac{\theta}{2}-1

    -----> 2 \cos^2 \frac{\theta}{2}=1+\cos \theta



    Going back to the equation :

    5 \cos 2 \theta+(1+\cos \theta)+1=0

    But \cos 2 \theta=2\cos^2 \theta-1

    ---> 5 (2\cos^2 \theta-1)+\cos \theta+2=0

    10 \cos^2 \theta-5+\cos \theta+2=0

    \boxed{10 \cos^2 \theta+\cos \theta-3=0}


    Substitute y=\cos \theta and you're done


    If you still can't get to the solution, show your working
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  3. #3
    Super Member fardeen_gen's Avatar
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    Thanks moo. There is some problem with either my computer or the forum.I did not double post voluntarily. An extra post appeared earlier also with no fault of my own. Mods please take notice!
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