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Math Help - solving theta help

  1. #1
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    solving theta help

    <br />
12sin^2(2\theta)-5sin(2\theta)-3=0<br />

    My teacher said that there were going to be 8 possible solutions. I don't really understand what steps to take to get 8?

    i factored the equation down to

    3sin(2\theta)+1 and 4sin(2\theta)-3

    i get down to

    sin(2\theta)=-1/3 and sin(2\theta)=3/4

    i don't know what to do from here to come out with 8 solutions

    also the bounds for the equation are 0 (less than or equal to) theta (less than) 360
    Last edited by ldamnedl; December 3rd 2009 at 10:25 PM. Reason: forgot to mention the bounds
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  2. #2
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    Hello ldamnedl

    Welcome to Math Help Forum!
    Quote Originally Posted by ldamnedl View Post
    <br />
12sin^2(2\theta)-5sin(2\theta)-3=0<br />

    My teacher said that there were going to be 8 possible solutions. I don't really understand what steps to take to get 8?

    i factored the equation down to

    3sin(2\theta)+1 and 4sin(2\theta)-3

    i get down to

    sin(2\theta)=-1/3 and sin(2\theta)=3/4

    i don't know what to do from here to come out with 8 solutions

    also the bounds for the equation are 0 (less than or equal to) theta (less than) 360
    Your working is fine. Note next, that if 0^o\le\theta<360^o, then 0^o\le2\theta<720^o. So we have two equations to solve for values of 2\theta in this range; then divide these answers by 2 to get the values of \theta. I'll start you off:
    \sin2\theta = -\frac13

    \Rightarrow 2\theta = 180 + 19.47,\; 360 - 19.47,\; 540+19.47,\; 720 - 19.47
    = 199.47, ...
    \Rightarrow \theta = 99.7^o, ...
    Can you complete it now?

    Grandad
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