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Home > A2C > Chapter 8 > Lesson 8.2.2 > Problem 8-127

8-127.

Find an equation for each graph below.    

  1. Repeating wave curve, first visible, low & high points: (negative pi fourths, comma 1) & (3 pi fourths, comma 3), continuing to repeat the wave, with the following highlighted points: (pi fourths, comma 2), (5 pi fourths, & (9 pi fourths, comma 2).

    Use the general equation .
    Determine the value for each of the three parameters.

    First identify a convenient locator point.
    In this case, we will use:

    The value of the point represents the horizontal shift.
    The value of the point represents the vertical shift.

    The amplitude (a) is the distance from the midline to the highest point.
    In this case and the highest point is , so .
    Since the graph increases from the locator point in the same way does, a is positive.

  1. Repeating wave curve, first visible, low & high points: (negative pi , comma negative 1) & (0, comma 1), continuing to repeat the wave, with the following highlighted points: (negative pi halves, comma 1 half), & (pi halves, comma 1 half).

    See part (a).
    Pay careful attention to the scale on the -axis when determining and .

  1. Repeating wave curve, first visible low & high points: (negative 3 pi fourths, comma 1) & (negative pi thirds, comma 3), continuing to repeat the wave, with the following highlighted points: (negative 5 pi sixths, comma 2),  (pi sixth, comma 2), & (7 pi sixth, comma 2).

    If you choose  as your locator point, notice the first cycle of the graph is an inverted sine curve, so the a value will be negative.

    See part (a).

  1. Repeating wave curve, first visible high & low points: (negative 5 pi sixths, comma 2) & (pi sixths, comma negative 4), continuing to repeat the wave, with the following highlighted points: (negative pi thirds, comma negative 1),  (2 pi thirds, comma negative 1), & (5 pi thirds, comma negative 1).

    See parts (a) and (c).