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Math Help - need help finding how man solutions there are please.

  1. #1
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    need help finding how man solutions there are please.

    how many solutions are there on the interval [0,2pi]?
    cos(x)sin(x)+3cos(x)+sin(x)+3=0

    Im looking at this problem and Im just lost.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Here is a hint

    Note that it can be rewritten as

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

    Now factor by grouping to get

    \sin(x)[\cos(x)+1]+3[\cos(x)+1]=(\cos(x)+1)(\sin(x)+3)=0

    Now use the zero factor principle to solve.
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