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IM Alg2.6.13 Lesson: Amplitude and Midline

Match each equation to its graph. Be prepared to explain how you know which graph belongs with each equation.

Suppose a windmill has a radius of 1 meter and the center of the windmill is (0,0) on a coordinate grid.

Write a function describing the relationship between the height  of  and the angle of rotation . Explain your reasoning.

Describe how your function and its graph would change if the windmill blade has length 3 meters.

Describe how your function and its graph would change if the windmill blade has length 0.5 meter.

Test your predictions using graphing technology.

A windmill has radius 1 meter and its center is 8 meters off the ground. The point  starts at the tip of a blade in the position farthest to the right and rotates counterclockwise. Write a function describing the relationship between the height  of , in meters, and the angle  of rotation.

Graph your function using technology.

How does it compare to the graph where the center of windmill is at ?

What would the graph look like if the center of the windmill were 11 meters off the ground? Explain how you know.

Here is the graph of a different function describing the relationship between the height y, in feet, of the tip of a blade and the angle of rotation θ made by the blade.

Describe the windmill.