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Math Help - Trig Equation

  1. #1
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    Exclamation Trig Equation

    If you could help with these thanks!

    #1) 2sin^2X=sinX

    #2) cosX=sinX

    #3) tanX+secX=1
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  2. #2
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    Quote Originally Posted by amanda0603 View Post

    #1) 2sin^2X=sinX

    2\sin^2{x} - \sin{x} = 0

    \sin{x}(2\sin{x} - 1) = 0

    set each factor equal to 0 and solve for x



    #2) cosX=sinX

    solve this one by looking at your unit circle



    #3) tanX+secX=1

    \sec{x} = 1 - \tan{x}

    square both sides ...

    \sec^2{x} = 1 - 2\tan{x} + \tan^2{x}

    1 + \tan^2{x} =  1 - 2\tan{x} + \tan^2{x}<br />

    0 = -2\tan{x}

    solve for x
    .
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  3. #3
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    Quote Originally Posted by skeeter View Post
    .
    Alternatively for #2, divide both sides by \cos{x} to give

    1 = \tan{x}.

    Solve for x.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    Alternatively for #2, divide both sides by \cos{x} to give

    1 = \tan{x}.

    Solve for x.
    o.k. in this particular equation, but not always a good idea in general as cos{x} = 0 may be a possible solution in another equation.
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  5. #5
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    Quote Originally Posted by amanda0603 View Post
    If you could help with these thanks!

    #1) 2sin^2X=sinX

    #2) cosX=sinX

    #3) tanX+secX=1
    #1) 2sin^2x = sinx
    2sin^2x - sinx = 0
    sinx (2sinx - 1) = 0
    sinx = 0
    x = 0, 180, 360

    2sinx - 1 = 0
    2sinx = 1
    sinx = 1/2
    x = 30, 150

    0verall: 0, 30, 150, 180, 360

    #2) cosx = sinx

    cosx - sinx = 0
    1 - tanx = 0
    tanx = 1
    x = 45, 225
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