firstly, i check the x_rotation and y_rotation by using

/data get entity @s

i see that the range of X is from -360 to 360 and the range if Y is from -90 to 90

and then, i use

/execute as @s[x_rotation=-45..45] run say SOUTH  &  /execute as @s[y_rotation=-45..45] run say STRAIGHT(as i am turning at the right rotation)

and it worked !!!

but later, i use

/execute as @s[x_rotation=-135..-45] run say EAST  &  /execute as @s[y_rotation=-90..-45] run say UP  &  other commands to check the rotation(even i am turning at the right rotation)

but it didn't worked !!!

i don't know whether i'm using the fault command or the minecraft cannot check the number from -180 to -45 and from 180 to 45 ???