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 [math]h[/math] of [math]W[/math] and the angle of rotation [math]\theta[/math]. Explain your reasoning.[br]

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

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

Test your predictions using graphing technology.

[size=150]A windmill has radius 1 meter and its center is 8 meters off the ground. The point [math]W[/math] starts at the tip of a blade in the position farthest to the right and rotates counterclockwise. [br][br][/size]Write a function describing the relationship between the height [math]h[/math] of [math]W[/math], in meters, and the angle [math]\theta[/math] of rotation.

Graph your function using technology.

How does it compare to the graph where the center of windmill is at [math]\left(0,0\right)[/math]?[br]

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

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.