-lm doesnt work unless it's at the end of the command [duplicate]

Answer 1

-lm needs to be at the end of the command, most likely in the first case with the literal the compiler is optimizing out the call to any function and therefore does not need to link against the library. This is called constant folding and for example we can see in the gcc docs on Other Built-in Functions Provided by GCC says:

GCC includes built-in versions of many of the functions in the standard C library. The versions prefixed with __builtin_ are always treated as having the same meaning as the C library function even if you specify the -fno-builtin option. (see C Dialect Options) Many of these functions are only optimized in certain cases; if they are not optimized in a particular case, a call to the library function is emitted.

Answer 2

This would be explained if your instructors are using gold and you are using GNU ld. These are two linkers, both are part of the GNU project, and both are commonly used with GCC.

If you are using GNU ld, you get the "traditional" behavior:

The order of specifying the -L and -l options, and the order of specifying -l options with respect to pathname operands is significant.

This means that you have to put -lm after any object files and libraries that depend on it.

However, if you are using gold, the -l options may appear first.

If you have gold installed on your system, you can test it yourself.

Here is what I get:

$ gcc -lm program.c 
/tmp/ccJmBjmd.o: In function `main':
program.c:(.text+0x15): undefined reference to `sin'
collect2: error: ld returned 1 exit status

But if I use gold, it works fine:

$ gcc -lm program.c -fuse-ld=gold