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Mr Davis 97

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Mr Davis 97

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They are called second order because they include all terms of the Taylor series up to and including the term of order two, so that any discrepancy is of third order. Note that the second order terms are zero for sine and tan.

- #3

Mr Davis 97

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So for sin and tan are the second and first-order approximations the same? And for cos, are the zeroth and first-order approximations the same?They are called second order because they include all terms of the Taylor series up to and including the term of order two, so that any discrepancy is of third order. Note that the second order terms are zero for sine and tan.

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YesSo for sin and tan are the second and first-order approximations the same? And for cos, are the zeroth and first-order approximations the same?

- #5

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$$\sin x=x+\mathcal{O}(x^3).$$

Then it's clear that the next term in the expansion is at order ##x^3##.

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