
06546553
j
2016b.00612
Miles, David
Improving an approximate formula.
Math. Sch. (Leicester) 40, No. 3, 29 (2011).
2011
Mathematical Association (MA), Leicester
EN
G60
N50
trigonometry
trigonometric functions
tangent
function values
approximate values
rational approximations
rational functions
percentage error
From the text: In a recent issue of this journal, [M. Rose, ``Miscellany", ibid. 39, No. 1, 27 (2010)] offered an interesting approximate formula: $\tan x =\frac{10+x}{100x} (25\le x\le 65)$. But can we improve this formula without resorting to calculus? It seems reasonable to assume that a more accurate formula might take the form: $\tan x =\frac{x^2+Ax+B}{x^2+Cx+D}$.