It seems that the promoter regions are written from the 5' to 3' direction. My lecture notes, for example, give the -35 and -10 promoter regions sequences like so:
Wikipedia seems to agree, on their article about promoters.
However, RNA polymerase transcribes in the 3' to 5', as in it reads the template strand in the 3' to 5' direction. In that case, why aren't the promoter regions written also in the 3' to 5' direction?
Meaning, instead of the -10 sequence being
5'-TATAAT-3', why is it not
3'-ATATTA-5', in agreement with the direction of transcription?
My intuitive guess is that the $\sigma$ factor recognises the promoter region in a 5' to 3' directionality. But I cannot find any information to back up this guess. Additionally, if this is true, how could it have been determined (experimentally)? Furthermore, whatever the answer is, does it also apply to transcription in eukaryotes?