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Math Help - Trigonometric Equation

  1. #1
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    Trigonometric Equation

    Solve the equation between 0 \leq \theta \leq 360 for
    tan^2\theta + 2sec\theta = 7

    My answers for this:
    \theta = 60, 300, 104.5, 244.5.
    Are these values correct? I am new to these trigonometric identities and if I have this right then it's definitely a step in the right direction.
    If not, then I'll post my working to try and find out where I went wrong.
    Thanks if you can help
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  2. #2
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    Hello, db5vry!

    Except for a bit of arithmetic, good work!


    My answers for this: \theta \:= \:60^o,\;300^o,\;104.5^o,\;{\color{red}\rlap{/////}}244.5^o

    That last angle should be: 255.5^o

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  3. #3
    Senior Member I-Think's Avatar
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    tan^2\theta + 2sec\theta = 7

    (* by cos^2\theta):sin^2\theta+2cos\theta=7cos^2\theta
    8cos^2\theta-2cos\theta-1=0
    (4cos\theta+1)(2cos\theta-1)=0
    cos\theta=-0.25,+0.5

    \theta=60,300,104.478,255.522

    Yep, your answers are correct.
    N.B. A better place to check your answers to trigonometric equations are your nearest local calculator, which will probably be a distance of a few keystrokes away from you when you read this
    Edit
    I'm a bit late, and it seems I missed your slight error, my apologies on the latter
    Last edited by I-Think; June 11th 2009 at 12:09 PM. Reason: Late
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