Each trig function has a base range, or domain. Everything beyond that range is just multiples of pi or repeats of previous values, depending on the function. A lookup table is an array of values that you can use to store this base range. For instance, lets say you were using the "Sine" function to compute your locations. You could create an array variable(lets call it SINLOOKUP) in memory containing the values of the sine function, such that where X is equal to the numerical count of the array (SINLOOKUP[X]), the value of SIN(X) is stored in that spot. Now when you need to know what the sine value is of 47, you just "look up" item number 47 in your array. Basically: SINLOOKUP[X] = sin(X). You can also do the same thing a variety of other ways depending on your processors capabilities.