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That is (the cosin I mean), the abscissa of a generic point P along the circumference or the lenght of the perpendicular projection of P onto the ordinate, is given by the ratio of the adjacent cathetus to the hypotenus? The same question can be asked about the sinus obviously; is it something to be taken just as it is, as a matter of fact, a definition?

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Yes, cosine is defined as the ratio of the adjacent side to the hypotenuse of a right angled triangle – Elements in Space Dec 15 '12 at 12:12
Now also dig up the definitions of hypothenuse, triangle, right angle ... – Hagen von Eitzen Dec 15 '12 at 12:14

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