FIGURE 16.4 Illustration of the inverse tangent function.

The goal is to find the solution of x as y is incremented in the range (0,1). Clearly, x approaches infinity as y approaches unity, so that the goal is to generate the x(y) relationship accurately as close as possible to y=1. The curve appears as shown in Figure 16.4. As y is incremented by small amounts just below unity, the differences in x due to the increment are large, so that the solution value is far from the initial iterate.