So i tried starting from scratch.
I started a new project with a new name.
Main.c and rap.h are both in the C:\cygwin\home\eb\rap02 directory.
I have also entered 'C:\cygwin\home\eb\rap02' into Search directories->[tab]Compiler (under Global compiler settings).
The Selected compiler is still Cygwin GCC.
So now main.c contains '#include rap.h' and with Compiler logging set to Full command line my Build log says:
-------------- Build: Debug in rap02 ---------------
x86_64-w64-mingw32-gcc.exe -Wall -g -IC:/cygwin/home/eb/rap02 -c C:/cygwin/home/eb/rap02/main.c -o obj/Debug/main.o
cygwin warning:
MS-DOS style path detected: C:/cygwin/home/eb/rap02/main.c
Preferred POSIX equivalent is: /cygdrive/c/cygwin/home/eb/rap02/main.c
CYGWIN environment variable option "nodosfilewarning" turns off this warning.
Consult the user's guide for more details about POSIX paths:
http://cygwin.com/cygwin-ug-net/using.html#using-pathnamesC:/cygwin/home/eb/rap02/main.c:10:17: fatal error: rap.h: No such file or directory
compilation terminated.
Process terminated with status 1 (0 minutes, 0 seconds)
1 errors, 0 warnings