If asked to write a computer program or design a central processing unit to compute the sine or cosine of any given angle x, the programmer or chip designer would not necessarily reference a table of trigonometric values. Rather, the person charged with such a task would return to calculus, Taylor’s TheoremTaylor’s theorem, and the associated series. In particular, the Taylor series for the sine and cosine functions are sin(x) =  \(x - \tfrac{1}{3!}x^{3} + \tfrac{1}{5!}x^{5} - \tfrac{1}{7!}x^{7} + \tfrac{1}{9!}x^{9} \cdots\) and cos(x) =  \(1 - \tfrac{1}{2!}x^{2} + \tfrac{1}{4!}x^{4} - \tfrac{1}{6!}x^{6} + \tfrac{1}{8!}x^{8} \cdots\) .