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Home > PC3 > Chapter 3 > Lesson 3.1.5 > Problem 3-82

3-82.

Write one equation in terms of sine and one equation in terms of cosine for the graph shown at right.  

Periodic curve, x axis scaled from negative 2 pi to 2 pi, with 4 visible turning points, at (negative 3 halves pi, comma negative 2), (negative 1 half pi, comma 4), (1 half pi, comma negative 2), & (3 halves pi, comma 4).

Where is the midline of the curve? This is the vertical shift of the function.

Added to original periodic curve, horizontal line at, y = 1.

What is the amplitude?

Added: Vertical segment from horizontal line, y = 1, to second turning point.

What is the simplest horizontal shift for the sine?

Added: highlighted point at, (pi, comma 0).

What is the simplest horizontal shift for the cosine?

Added: highlighted point at, (negative 1 half pi, comma 4).