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Alternate Definitions of Sine and Cosine


If tex2html_wrap_inline715 is an acute angle, then we can draw a right triangle, as in (A) of the figure below. The side opposite the angle tex2html_wrap_inline715 is labeled b, the side adjacent to tex2html_wrap_inline715 is labeled a and the hypotenuse is labeled c. In (B), we have placed the vertex A at the origin, and the adjacent side on the x-axis. The vertex B is at the point (a,b).

acute.epsAlternate definitions for tex2html_wrap_inline735 and tex2html_wrap_inline725 are:



Note that when c=1, the point B(a,b) lies on the unit circle, and tex2html_wrap_inline993 is the second coordinate of the point B(a,b), while tex2html_wrap_inline997 is the first coordinate of this point. Thus these alternate definitions are consistent with the old definitions of sine and cosine.

Carl Lee
Wed Apr 21 08:17:28 EDT 1999