Verify that if we take only the terms up to and including x2n−1/(2n−1)! in the series (2) for sin x and if |x| <√ 6, then the error involved does not exceed |x|2n+1/(2n+1)!. How many terms are needed to compute sin(23) with an error of at most 10−8? What problems do you foresee in using the series to compute sin(23)? Show how to use periodicity to compute sin(23). Show that each term in the series can be obtained from the preceding one by a simple arithmetic operation.
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