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Thread: 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 : $\displaystyle \sec^2 \theta=1+\tan^2 \theta$
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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 $\displaystyle sec^2(\theta)$ with $\displaystyle 1+ tan^2(\theta)$ in your equation.

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

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

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

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