coordinate.c running 
first quadrant 
convert  x1=0.500000, y1=0.700000 
   to polar  r=0.860233, theta=0.950547 

convert  r=0.860233, theta=0.950547 
   to cartesian  x=0.500000, y=0.700000 
        theta=54.462322 degrees 

second quadrant 
convert  x2=-0.800000, y1=0.700000 
   to polar  r=1.063015, theta=2.422763 

convert  r=1.063015, theta=2.422763 
   to cartesian  x=-0.800000, y=0.700000 
        theta=138.814075 degrees 

third quadrant 
convert  x2=-0.800000, y2=-0.500000 
   to polar  r=0.943398, theta=-2.582993 

convert  r=0.943398, theta=-2.582993 
   to cartesian  x=-0.800000, y=-0.500000 
        theta=212.005383 degrees 

fourth quadrant 
convert  x1=0.500000, y2=-0.500000 
   to polar  r=0.707107, theta=-0.785398 

convert  r=0.707107, theta=-0.785398 
   to cartesian  x=0.500000, y=-0.500000 
        theta=315.000000 degrees 

convert  x1=0.500000, y1=0.700000, z1=0.800000 
   to cylindrical  r=0.860233, theta=0.950547, zs=0.800000 

convert  r=0.860233, theta=0.950547, zs=0.800000 
   to cartesian  x=0.500000, y=0.700000, z=0.800000 

convert  x2=-0.800000, y2=-0.500000, z2=-0.700000 
   to cylindrical  r=0.943398, theta=-2.582993, zs=-0.700000 

convert  r=0.943398, theta=-2.582993, zs=-0.700000 
   to cartesian  x=-0.800000, y=-0.500000, z=-0.700000 

first octant 
convert  x1=0.500000, y1=0.700000, z1=0.800000 
   to spherical  r=1.174734, theta=0.950547, phi=0.821662 

convert  r=1.174734, theta=0.950547, phi=0.821662 
   to cartesian  x=0.500000, y=0.700000, z=0.800000 
        theta=54.462322 degrees, phi=47.077755 degrees 

seventh octant 
convert  x2=-0.800000, y2=-0.500000, z2=-0.700000 
   to spherical  r=1.174734, theta=-2.582993, phi=2.209157 

convert  r=1.174734, theta=-2.582993, phi=2.209157 
   to cartesian  x=-0.800000, y=-0.500000, z=-0.700000 
        theta=212.005383 degrees, phi=-53.424640 degrees 

first hypertant 
convert  x1=0.500000, y1=0.700000, z1=0.800000, t1=0.900000 
   to spherical  r=1.479865, theta=0.950547, phi=0.821662, psi=0.917051 

convert  r=1.479865, theta=0.950547, phi=0.821662, psi=0.917051 
   to cartesian4D  x=0.500000, y=0.700000, z=0.800000, t=0.900000 
        theta=54.462322 degrees, phi=47.077755 degrees, psi=52.543160 degrees 

finished coordinate.c