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Program 1
 

public class Circle {

  static private double sines[] = new double[1000]; 
  static private double cosines[] = new double[1000]; 

  // Pre calculation of sines and cosines:
  static {
    double deltaX = (Math.PI/2)/(1000-1);
    double x;
    int i; 
    for(i=0, x = 0.0; i < 1000; i++, x = x+deltaX){
      sines[i] = Math.sin(x);
      cosines[i] = Math.cos(x);
    }
  } //end static

  // Circle operations: Use sines[x] instaed of the static method Math.sin(x) 
  // and cosines[x] instead of the static method Math.cos(x).

  // ...
}