Sine and Cosecant Functions (Special Property)

Suppose

is an angle drawn in standard position. Let P(x, y) be any point in the coordinate plane and let r = the distance from P to the origin. Recall

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 P lies, what is the relationship between the values of the ratios and ?

Regardless of where P lies, what is the relationship between the values of the ratios and ?

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