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Circular function help please?

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  • 1 month ago

    (b)  g(x) = pi*cos[(1/3)x] + pi.

    h = (1/3), k = pi, m = pi.

    (c)  It may be easier to start (c) before (a).

    y = f(x) = a*arcos[(x + b)/c] =>

    y/a = arcos[(x + b)/c] =>

    cos(y/a) = (x + b)/c =>

    c*cos(y/a) - b = x.

    Now it's easier (for me) to see the values of a,b,c by looking at the graph "sideways."  However, it's hard to tell whether the "f" curve is supposed to represent a full half-cycle, as it doesn't really appear tangent to the y-axis in the problem.  If it is intended to be tangent to the y-axis (i.e., vertical at y = 10pi), then a = 1/10, b = -15pi/2, and c = 15pi/2.

    And the answer to (c) is 

    x = (15pi/2)*cos(y/10) + 15pi/2.

    (a)  x - 15pi/2 = (15pi/2)*cos(y/10) =>

    y = 10*arcos[(x - 15pi/2)/(15pi/2)] = f(x) =>

    a = 10, b = -15pi/2, c = 15pi/2.

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