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Precalculus

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2sin^2x+3cosx=3 find all solutions in the interval [0,2pi]

  • Precalculus - ,

    Use the identity sin²(x)=1-cos²(x).

    So
    2sin^2x+3cosx=3 becomes
    2cos²(x)-3cos(x)-1=0

    Solve the quadratic for cos(x),
    I get cos(x)=1 or cos(x)=1/2

    On the interval [0,2π], each value of cos(x) has two solutions for a total of 4 values of x.

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