PreCalculus/Trigonometry graphing and equations?

Write the positive sine y = d + asin(bx - c) and cosine y = d + acos(bx - c) functions for the graph.

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    Period is 4pi/8, or pi/2

    Amplitude is 2

    Axis of symmetry is y = 0

    y = 0 + 2 * sin(bx - c)

    y = 2 * sin(bx - c)

    No horizontal shift here.  c = 0

    y = 2 * sin(bx)

    b = 1, then period is 2pi

    b = 2, then period is pi

    so

    period is 2pi / b

    2pi / (pi/2) =>

    4

    y = 2 * sin(4x)

    Guess what?  It'll be mostly the same for cosine as well.  It'll just be shifted

    y = 2 * cos(4x - c) + 0

    y = 2 * cos(4x - c)

    It's shifted pi/8 units to the right.  But we have to do something first.  We have to rewrite this as:

    y = 2 * cos(4 * (x - c))

    Where c is our shift to the right.

    4 * pi/8 = pi/2

    y = 2 * cos(4x - pi/2)

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