WOLFRAM|DEMONSTRATIONS PROJECT

Continued Fraction Approximations of the Tangent Function

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continued fraction terms
tan(x)≈
1
1
x
-
1
3
x
-
1
5
x
+
1
7
Many elementary and special functions have nice continued fraction approximations. This Demonstration allows investigation of the continued fraction approximation of the tangent function. Because any finitely truncated continued fraction approximation is a rational function, it cannot approximate the periodic tangent function globally. But the range of good approximation increases with the number of terms.