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March 26, 2017

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By what fraction of the period of f(x)=10 cos(7 x) has the graph of f(x) been shifted to obtain the graph of g(x)=10 cos(7x- pi/2). how do I approach this and solve for the fraction shift and the domain and range?

  • trig - ,

    2 pi is a whole circle or period
    pi/2 is a quarter of a circle or period

    the domain of this function is all real x, in other words x can be any real number positive or negative
    However cosine is between -1 and +1 so range is between -10 and +10

  • trig - ,

    the period of y = 10cos(7x) is 2π/7

    rewriting the second as
    y = 10cos 7(x - π/14) we can see that the phase shift was
    π/14 to the right.

    so what fraction is that phase shift of the period?
    (π/14)/(2π/7)
    or
    1/4 of the phase shift.

  • trig - ,

    humm, looks like we agree in the end :)

  • Damon - trig - ,

    Damon, when I opened the page and started to answer this question, I left it alone to watch the end of the WorldCup football game, and when I resumed I did not refresh the page, thus did not see your answer was already posted.

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