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HallsofIvy
#6
Mar9-12, 01:01 PM
Math
Emeritus
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if you are asking about the connection between the "circular" functions (sine and cosine as defined using the unit circle) and the "trigonometric functions) (sine and cosine as defined using right triangles), from a point, (x, y), on the unit circle, draw the line from (x, y) to (0, 0), the line from (x, y) to (x, 0), and the line from (x, 0) to (0, 0).

That gives a right triangle which has "near side" of length x, "opposite side" of length y, and hypotenuse of length 1. Therefore, [itex]sin(\theta)=[/itex]"opposite side over hypotenuse= y/1= y and [itex]cos(\theta)= [/itex]"near side over hypotenuse"= x.

(Since the angles in a triangle can only be between 0 and 90 degrees, we really have to assume that (x, y) is in the first quadrant. The circle definition extends that to all real numbers.)