From the text: In a recent issue of this journal, [M. Rose, â€śMiscellany", ibid. 39, No. 1, 27 (2010)] offered an interesting approximate formula: $\tan x =\frac{10+x}{100-x} (25\le x\le 65)$. But can we improve this formula without resorting to calculus? It seems reasonable to assume that a more accurate formula might take the form: $\tan x =\frac{x^2+Ax+B}{x^2+Cx+D}$.