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Home > PC > Chapter 4 > Lesson 4.2.4 > Problem 4-114

4-114.

Find an equation for each graph below. 

  1. Periodic curve, x axis scaled from negative 2 pi to 2 pi, 9 visible turning points, first at (negative 2 pi, comma 2), second at (negative 3 halves pi, comma negative 4), y intercept at (0, comma 2).

  1. Periodic curve, x axis scaled from negative 2 pi to 2 pi, 2 visible turning points, first at (negative pi, comma 2), second at (pi, comma negative 2), y intercept at the origin.

General Steps:
1. Choose either sine or cosine curve.
2. Locate the midline and determine amplitude.
3. The midline is the vertical shift.
4. Find the horizontal shift.
5. Find the period and calculate the frequency: .
6. Add a negative before 'a' if the function was vertically reflected.

Then put the information in the form below.
The cosine function has the same general equation as the sine function.
The general equation for sine is, y = a sine of open parenthesis, b, open parenthesis, x minus h, close parenthesis twice + k, a = amplitude, b = angular frequency, h = horizontal shift, and k = vertical shift. The product of the period, p, and the angular frequency, b, is 2 pi, p b = 2 pi.

Use the eTool below to visualize this problem.
Click on the link to the right to view the full version of the eTool: PCT 4-114 eTool

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