Trigonometrical functions Numerical values

Floiy (155) and other American writers use the opposite convention making 8 = 0° for the trans or anti conformation. As a result the numerical values of the torsion angles reported here are often different from those reported in the original literature. Differences are found in the formulas involving trigonometrical functions and in the appearance of energy maps. Specific conventions are used for vinyl polymers. 

This, however, does not mean that we would not have to work exponentially hard actually to obtain Xn if an explicit numerical value is required. This is so because of the occurrence of the factor 2 in (1.2.6) in conjunction with the trigonometric function sin which is n periodic. The periodicity of the sin function, which effectively truncates the leading decimal figures in its argument, requires that we have to keep exponentially many decimal digits in xq in order to produce the leading decimal figures of More about this mechanism that is at the heart of chaos can be found in Section 2.2. 

The numerical value of the gamma function has been tabulated for all values of n between 1 and 2 to twelve decimal places. By the aid of such a table, the approximate value of all definite integrals reducible to gamma functions can be calculated as easily as ordinary trigonometrical functions, or logarithms. There are four cases ... 

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