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Although sums, differences, and averages are easy to compute with high precision, even by hand, trigonometric functions and especially inverse trigonometric functions are not. For this reason, the accuracy of the method depends to a large extent on the accuracy and detail of the trigonometric tables used. For example, a sine table with an entry for each degree can be off by as much as 0.
Tables were painstakingly constructed for prosthaphaeresis with values for every second, or th of a degree. One solution is to include more table values in this area. For example, would become 0.
Another effective approach to enhancing the accuracy is linear interpolation , which chooses a value between two adjacent table values. The actual sine is 0.
A table of cosines with only entries combined with linear interpolation is as accurate as a table with about entries without it. Even a quick estimate of the interpolated value is often much closer than the nearest table value. See lookup table for more details. Reverse identities[ edit ] The product formulas can also be manipulated to obtain formulas that express addition in terms of multiplication.
Although less useful for computing products, these are still useful for deriving trigonometric results: sin.
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