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 ?

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

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