If is an acute angle, then we can draw a right triangle, as in (A) of the figure below. The side opposite the angle is labeled b, the side adjacent to 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 and are:
Note that when c=1, the point B(a,b) lies on the unit circle, and is the second coordinate of the point B(a,b), while is the first coordinate of this point. Thus these alternate definitions are consistent with the old definitions of sine and cosine.