The best way to get an approximation that converges quickly is if |x – a| < 1. As we saw in class the easiest values to plug
in for a when approximating sine or cosine are the numbers ½πk, one of which will be less than 1 away from any real number chosen. For the following values of x, we will approximate cos x, finding the closest integer multiple of ½π, the approximation s(7) written to nine places after the decimal and the base ten exponent of the error cos(x) – s(7).
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