/*

   Start with the function  Y = 1/X sin(X).   We want the inverse of this
   function.  That is given a value for Y find the X that corresponds to
   this Y value.

   The equation  Y = 1/X sin(X)  can not be inverted analytically so this
   routine will use a method of successive approximation to determine the
   value of X that corresponds to the supplied value of Y.  This work is
   greatly simplified because this routine only needs to be able to work
   over a limited range of X.  This range is the first quadrant were X
   can have any value in the range   0 <= X <= Pi/2   i.e. 0 to 90 degrees.

   In this range of X, Y takes the values 1 at X=0 (0 degrees) through
   2/Pi at X = Pi/2 (90 degrees).  Through this range of X, Y is
   monotonically falling from its value of 1 down to 2/Pi.

   The very well behaved nature of this function in this range makes it
   easy to use successive approximation.  The following algorithm is used:


        The routine is called and passed the value of Y.
        Set working fraction to 1/2.
        Set the guessed value of X to Pi/4  i.e. 45 degrees.

     1. Test is Y is <=>  1/X sin(X)  using the guessed value of X.

     2. If Y < 1/X sin(X) then the new guessed value of X equals the
        current guessed value + (Pi * Working_Fraction).
        New Working_Fraction equals 1/2 of the current Working_Fraction.

     3. Else If Y > 1/X sin(X) then the new guessed value of X equals the
        current guessed value - (Pi * Working_Fraction).
        New Working_Fraction equals 1/2 of the current Working_Fraction.

     4. Exit if Working_Fraction is small enough, else go to step 1.


   The advantage of this method of starting in the middle and each time
   dividing the step size by 2 is that one does not have to worry about what
   to do at X = 0 where the function becomes undefined.




   Calculate and display    1/X  sin(X)

   for   0 < X < PI/2

*/

#include <math.h>
#include <stdio.h>

main ()

{

        float  lower,  upper,  step          ;
        float  temp_1, temp_2, temp_3        ;

        lower =   0.025  ;
        upper =   1.550  ;
        step  =   0.025  ;

        printf ("\n Degrees,  Radians,  1/X sin(X) \n" );

        temp_1  =  lower  ;

        while (temp_1 <= upper)  {

                temp_2 = ( 1.0 / temp_1 )  *  sin(temp_1)  ;

                temp_3 = temp_1 * 57.295779                ;

                printf (" %4.2f     %4.3f       %6.3f \n",
                                                  temp_3, temp_1, temp_2 );

                temp_1 = temp_1 + step  ;
        }
}