Get latitude and longitude from X and Y coordinates

Question

It seems that there is a wealth of knowledge on converting from Longitude and Latitude to X and Y coordinates, but not the reverse.

Here is a function of mine based

Answer 1

Ok based on the math @ Wikipedia, I managed to reverse the equation

  // find latitude from Y coord
    // height / 2 to make middle of map ZERO, *-1 to flip it, so south of equator is negative.
    // divide by FACTOR to make it fit within bounds of larger map
  float reMapY = ((mouseY - (height/2))*-1)/FACTOR;
  println(degrees(reMapY));

  // I have no idea what I'm doing
  float temp = sqrt((pow(PI,2)/3 - pow(reMapY,2)));
  float reMapX = (mouseX - (width/2))/FACTOR;
  float temp2 = ((reMapX / temp) * TWO_PI) / 3;
  println(degrees(temp2));

Just remember that FACTOR is something inherent in my design, because of the size of my map. I believe it should be width = 5.47 * FACTOR.