Converting from heliocentric coordinate system with coordinates in arcsec to coordinates in longitude latitude

Script

double x = Double.parseDouble(xString);
double y = Double.parseDouble(yString);
double b0 = Double.parseDouble(b0String);
double sunr = Double.parseDouble(sunrString);

debug = "inputs: x, y, b0, sunr " + x + " " + y + " " + b0+ " " + sunr +"\n" ;

double rho = Math.hypot(x,y);

if(rho > sunr){
  rho=sunr;
}
debug = debug + "rho" + rho + "\n";

double outrho = rho / sunr;

double arcsec2rad = 4.84813681e-6;

debug = debug + "arcsec2rad" + arcsec2rad + "\n";


rho = Math.asin(Math.sin(rho*arcsec2rad)/Math.sin(sunr*arcsec2rad)) - rho* arcsec2rad;

debug = debug + "rho" + rho + "\n";

double theta = Math.atan2(x,y);
debug = debug + "theta" + theta + "\n";
double srho = Math.sin(rho);
debug = debug + "srho" + srho + "\n";
double crho = Math.cos(rho);
debug = debug + "crho" + crho + "\n";
double ctheta = Math.cos(theta);
debug = debug + "ctheta" + ctheta + "\n";
double sb0 = Math.sin(b0);
debug = debug + "sb0" + sb0 + "\n";
double cb0 = Math.cos(b0);
debug = debug + "cb0" + cb0 + "\n";



double slat = sb0*crho +cb0* srho*ctheta;

if(slat>1.0){
  slat =1.0;
}
if(slat<-1.0){
 slat = -1.0;
}

debug = debug + "slat" + slat + "\n";

double radeg = 180/Math.PI;

lat = Math.asin(slat)*radeg;

lon = (Math.atan2(srho*Math.sin(theta), (crho*cb0-srho*sb0*ctheta)))*radeg;

debug = debug + "\n" + (srho*Math.sin(theta)) + " " + (crho*cb0-srho*sb0*ctheta);