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?
Why the cosin of an acute angle in a right-angled triangle
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trigonometry
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1Now also dig up the definitions of hypothenuse, triangle, right angle ... – 2012-12-15