RATIONAL TRIGONOMETRY: COMPUTATIONAL VIEWPOINT

Main idea behind rational trigonometry. Traditional trigonome-try uses non-algebraic functions such as sin(x) or cos(x) to solve triangles, i.e., to use the values of some of its parameters (sides a1, a2, a3, angles A1, A2, A3) for nding the values of others parame-ters. The use of non-algebraic functions complicates mathematical analysis, makes computations more difcult, and makes trigonome-try more difcult to learn. To avoid these difculties, N. J. Wildberger proposed to describe each side ai by its square si def = a2i (which he calls quadrance), and each angle Ai by its spread Qi def = sin2(Ai). In these terms, all the formulas become algebraic: e.g., the sine law takes the form s