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Math Help - Finding the general form....

  1. #1
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    Finding the general form....

    Today I was having a bit of a nostalgia moment when I came across an old problem then when I tried to solve it...well lets say it was harder than it seemed.

    Anyway the equation was:

    sin(3x) + cos(x) = 0

    And it asked you to find the general form of the solution...

    I have tried compound, double angle formulas but to no avail. I can graph it and find some solutions but not how to find a general form equation? Can someone please shoe me how to solve it?

    Cheers
    Lance

    EDIT:: Changed the - to a plus +
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  2. #2
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    [quote=Qwertyuiop23;514674]Today I was having a bit of a nostalgia moment when I came across an old problem then when I tried to solve it...well lets say it was harder than it seemed.

    Anyway the equation was:

    sin(3x) + cos(x) = 0

    And it asked you to find the general form of the solution...

    I have tried compound, double angle formulas but to no avail. I can graph it and find some solutions but not how to find a general form equation? Can someone please shoe me how to solve it?

    Cheers
    Lance

    cos(x) = -sin(3x) = cos(π/2 + 3χ)

    π/2 + 3x = 2nπ + or - ( x)

    Now solve for x .
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  3. #3
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    why 2n*pi?
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  4. #4
    Junior Member BobBali's Avatar
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    Trig

    Sin (3x) + Cos (x) = 0

    Cos(x) = -Sin(3x)
    Divide by Cos(x)

    - Sin(3x)/Cos(x) = 1
    * identity Sinx/Cosx = Tanx

    -Tan(2x) = 1

    Tan(2x) = -1

    2x = Tan^-1 (-1)

    Therefore, x = -22.5
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  5. #5
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    Quote Originally Posted by Qwertyuiop23 View Post
    why 2n*pi?
    If cos(x) = 1/2, then x = either 30 degrees or 330 degrees.

    In general, n*360 + or - (30).

    This is the general solution.
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