'Culinary,' 'cook,' and 'kitchen' all descend from Latin 'coquere' via completely different routes.
Of or relating to cooking or the kitchen.
From Latin 'culīnārius' (of or belonging to the kitchen), from 'culīna' (kitchen, cooking stove), an older form 'coquīna,' from 'coquere' (to cook), from PIE *pekw- (to cook, to ripen). The same PIE root produced English 'cook' (via Latin 'coquus' through Germanic), 'kitchen' (via Latin 'coquīna' through Germanic), 'concoct,' 'decoction,' and Greek 'peptein' (to cook, to digest — source of 'peptic' and 'pepsin'). The word 'culinary' preserves the Latin kitchen more faithfully than 'cook' does. Key
The English words 'cook,' 'kitchen,' and 'culinary' all derive from the same Latin root 'coquere' (to cook), but they arrived in English by completely different routes. 'Cook' came through Proto-Germanic borrowing from Latin 'coquus' before the Anglo-Saxons reached Britain. 'Kitchen' came through Old