Sly Requisitioner

Because improvise isn't an alternative cost, it can be used in conjunction with alternative costs.

Improvise can't pay for white mana , blue mana , black mana , red mana , green mana , or colorless mana mana symbols in a spell's total cost.

If an artifact you control has a mana ability with tap in the cost, activating that ability while casting a spell with improvise will result in the artifact being tapped when you pay the spell's costs. You won't be able to tap it again for improvise. Similarly, if you sacrifice an artifact to activate a mana ability while casting a spell with improvise, that artifact won't be on the battlefield when you pay the spell's costs, so you won't be able to tap it for improvise.