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Advanced Functions

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Consider the trig equation:

4sinxcos2x + 4cosxsin2x - 1 = 0

in the Interval [0, 2 pi]

Either show that there is no solution to the equation in this domain, or determine the smallest possible solution.

  • Advanced Functions -

    4sinxcos2x + 4cosxsin2x - 1 = 0
    4(sinxcos2x + cosxsin2x) = 1

    Did you recognize that the expression in my bracket matches with
    sin(A+B) = sinAcosB +cosAsinB ?

    so we have
    4(sin(x+2x)) = 1
    sin 3x = 1/4
    3x = .25268 radians
    x = .084227 radians

    (you wanted the smallest possible solution)

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