You're calculating the y-part of your new coordinate based on the 'new' x-part of the new coordinate. Basically this means your calculating the new output in terms of the new output...
Try to rewrite in terms of input and output:
vector2<double> multiply( vector2<double> input, double cs, double sn ) {
vector2<double> result;
result.x = input.x * cs - input.y * sn;
result.y = input.x * sn + input.y * cs;
return result;
}
Then you can do this:
vector2<double> input(0,1);
vector2<double> transformed = multiply( input, cs, sn );
Note how choosing proper names for your variables can avoid this problem alltogether!