Problem

Write a routine to compute sin x for x in radians as follows. First, using properties of...

Write a routine to compute sin x for x in radians as follows. First, using properties of the sine function, reduce the range so that π/2? x ?π/2. Then if |x| < 10⁻⁸, set sin x ≈ x; if |x| > π/6, set u = x/3, compute sin u by the formula below, and then set sin x ≈ [3 − 4 sin² u] sin u; if |x|?π/6, set u = x and compute sin u as follows:

Try to determine whether the sine function on your computer system uses this algorithm.

Note: This is the Pad´e rational approximation for sine.

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Solutions For Problems in Chapter 2.2

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