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Math Help - help solving the equation

  1. #1
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    help solving the equation

    hi wasnt sure whether the two questions should be together or seperate sorry if they were meant to got together

    solve the equation 3 sec^2 pheta +7= 11 tan pheta giving all values of x to 3sf in the interval 0<pheta<2pi

    sorry for the bad setting out dont no how to get pheta and pi signs

    thanks for any help
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  2. #2
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    Quote Originally Posted by mannilea View Post
    hi wasnt sure whether the two questions should be together or seperate sorry if they were meant to got together

    solve the equation 3 sec^2 pheta +7= 11 tan pheta giving all values of x to 3sf in the interval 0<pheta<2pi

    sorry for the bad setting out dont no how to get pheta and pi signs

    thanks for any help

    Use the identity : \sec^2 \theta=1+\tan^2 \theta
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  3. #3
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    thanks for the reply what could i word in google to get help on how to use the identity as i have never covered that
    thanks for any help
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  4. #4
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    Just replace sec^2(\theta) with 1+ tan^2(\theta) in your equation.

    3sec^2(\theta)+ 7= 11 tan(\theta) becomes
    1+ tan^2(\theta)+ 7= 11 tan(\theta)

    If you do not know how to solve that, replace tan(theta) with "x": 1+ x^2+ 7= 11x or x^2- 11x+ 8= 0. Can you solve that? Then use the fact that tan(\theta)= x to find \theta.
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  5. #5
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    Quote Originally Posted by HallsofIvy View Post
    Just replace sec^2(\theta) with 1+ tan^2(\theta) in your equation.

    3sec^2(\theta)+ 7= 11 tan(\theta) becomes
    1+ tan^2(\theta)+ 7= 11 tan(\theta)

    If you do not know how to solve that, replace tan(theta) with "x": 1+ x^2+ 7= 11x or x^2- 11x+ 8= 0. Can you solve that? Then use the fact that tan(\theta)= x to find \theta.
    but  3sec^2(\theta) = 3(1+tan^2(\theta)) = 3+3tan^2(\theta)
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