Proof of correctness:

Prove that:

1. The loop will stop in a finite number of steps.

2. The approximation y produced by the algorithm satsifies

Algorithm 1 sin(x) via Taylor series Input: r E IR; E R20 Output: an approximation y such that y Sin E Do y y-- (-1) 1r2K-1/(2k -1)! until 2k-+1 /(2k 1)! E return y