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Math Help - Solve for theta

  1. #1
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    Solve for theta

    Write all positive values within the interval of 0 degrees < \theta < 270 degrees

    1 - sec^{2} 2\theta - 3tan 2\theta = 0
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  2. #2
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    Quote Originally Posted by reiward View Post
    Write all positive values within the interval of 0 degrees < \theta < 270 degrees

    1 - sec^{2} 2\theta - 3tan 2\theta = 0
    Substitute \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1, simplify and solve the resulting simple trig equation.
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    Quote Originally Posted by mr fantastic View Post
    Substitute \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1, simplify and solve the resulting simple trig equation.
    <br />
1 - sec^{2} 2\theta - 3tan 2\theta = 0

    <br />
1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0

    \tan^2 (2 \theta)  - 3tan 2\theta = 0

    Im stuck. What do I factor it to?
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    Quote Originally Posted by reiward View Post
    <br />
1 - sec^{2} 2\theta - 3tan 2\theta = 0

    <br />
1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0

    \tan^2 (2 \theta) - 3tan 2\theta = 0 Mr F says: This is wrong. There is a careless mistake in signs.

    Im stuck. What do I factor it to?
    Factorise. Note that \tan (2 \theta) is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.
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    Quote Originally Posted by mr fantastic View Post
    Substitute \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1, simplify and solve the resulting simple trig equation.
    Quote Originally Posted by mr fantastic View Post
    Factorise. Note that \tan (2 \theta) is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.
    Oh okay.

     -\tan^2 (2 \theta) - 3tan 2\theta = 0

    Can I make that to  \tan^2 (2 \theta) + 3tan 2\theta = 0 ?

    If so, would the factor be  \tan(2 \theta) [tan + 3]= 0?
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    Quote Originally Posted by reiward View Post
    Oh okay.

     -\tan^2 (2 \theta) - 3tan 2\theta = 0

    Can I make that to  \tan^2 (2 \theta) + 3tan 2\theta = 0 ?

    If so, would the factor be  \tan(2 \theta) [tan + 3]= 0?
    Yes.
    Yes.
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