When a calculator computes the "sine" value of an angle there is a slight delay before the value is displayed. I was wondering if this delay is because the calculator is actually using a Taylor series expansion of the sine function and, thus, needs to keep adding terms until it reaches a term of "neglible" value.

Thanks...

The calculators may use a combination of look-up tables for certain values, and also use some kind of series or polynomial expansion to obtain the values for all other angles. Also needed are: normalization of the angle (reducing it to +/-180°); conversion between grad/rad/deg; use and truncation of guard digits; and checking for particular conditions (tangent of 90°, etc). These are the steps programmed in the calculator ROM or (not exactly named) microcode. In the HP Journal, between 1972 and 1977, some four or five articles appeared, detailing the methods chosen by the calculators designers for trig and log functions, and the trade-offs between execution time, error magnitude, and ROM space needed to implement them.

There is an algorithm called CORDIC (COordinate Rotation DIgital Computer) that is used to calculate trigonometric functions. If you want more information, try these:

http://www.ezcomm.com/~cyliax/Articles/RobNav/sidebar.html http://mvlsi.kaist.ac.kr/~fairwind/comarith/cordic_algo/cordic_algo.html