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Math Help - Which period is this function?

  1. #1
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    Which period is this function?

    This question is from the National University of Colombia entrance exam in 2006 (translated from Spanish).

    The function y=4cos(x/2) - 3sin2x is of period:

    A. π
    B, 4π
    C. 3π
    D. 2π

    I learned to divide the period of cos by 2π, so 2π/1/2 would be 4π I thought, and the period for the sin would be 2π/2 is π, and the least common number to divide into seems like it would make the answer 4π, but the answer sheet says D, 2π, and I can't figure out why. I have their entrance exam in two days and I need to understand all this. Please help me. Thank you
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  2. #2
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    The answer is B as this is the biggest period of 4cos(x/2) and 3sin2x


    In short find the individual period of both trig functions you are summing, the period of the summed functions will be the bigger of the 2.
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