To accurately approximate sin x and cos x for inclusion in a mathematical library, we
Chapter 8, Problem 8.4.14(choose chapter or problem)
To accurately approximate sin x and cos x for inclusion in a mathematical library, we first restrict their domains. Given a real number x, divide by to obtain the relation |x| = M + s, where M is an integer and |s| 2 . a. Show that sin x = sgn(x) (1)M sin s. b. Construct a rational approximation to sin s using n = m = 4. Estimate the error when 0 |s| /2. c. Design an implementation of sin x using parts (a) and (b). d. Repeat part (c) for cos x using the fact that cos x = sin(x + /2).
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