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→Error of the approximations: Clarified which version of the approximations were used to generate the plot "A Comparison of Approximation Errors". |
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==Error of the approximations==
[[File:Small angle compare error.svg|thumb|300px|A graph of the [[relative error]]s for the small angle approximations
Near zero, the [[relative error]] of the approximations {{tmath|\cos \theta \approx 1}}, {{tmath|\sin \theta \approx \theta}}, and {{tmath|\tan \theta \approx \theta}} is quadratic in {{tmath|\theta}}: for each order of magnitude smaller the angle is, the relative error of these approximations shrinks by two orders of magnitude. The approximation {{tmath|\textstyle \cos \theta \approx 1 - \tfrac12\theta^2 }} has relative error which is quartic in {{tmath|\theta}}: for each order of magnitude smaller the angle is, the relative error shrinks by four orders of magnitude.
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