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Tangent and Cotangent Functions (Special Property)

Suppose is an angle drawn in standard position. Let P(x, y) = any point in the coordinate plane, and r = distance from point P to the origin, then and . Interact with the applet below for a minute or two. Then answer the questions that follow. (Be sure to move point P to various locations!)

1.

Regardless of where point P lies, what relationship can you write about the ratios and ?

2.

Regardless of where point P lies, what relationship can you write about the ratios and ?

3.

What do these 2 observations imply about the tangent and cotangent functions? (Click here and/or here for a hint!)