oriens

Oriens, orientis, m., is the present participle of orior, "rise", doing duty as a noun. The full phrase is sol oriens, "the rising sun", and the sun drops out, leaving the participle to mean the quarter of the sky it rises in. Its opposite works the same way: occidens, "the setting sun", is the west.

Declines as a third-declension participle, ablative oriente when it is a noun, orienti when it is still functioning as one. In late and ecclesiastical texts Oriens with a capital is the eastern empire and then the eastern church, and it is that sense which reaches English as the Orient. Orientate is the same word doing something concrete: to orient a building was to point it east, which is why churches face where the sun comes up.