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.