As long as this artifact is untapped, each spell that would cost less than three mana to cast costs three mana to cast. (Additional mana in the cost may be paid with any color of mana or colorless mana. For example, a spell that would cost 1B to cast costs 2B to cast instead.)
If Trinisphere leaves the battlefield or becomes tapped or untapped as a cost to cast a spell, this cost is paid after you've locked in the total cost.
2020-08-07
To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions. Finally, apply Trinisphere's effect if the mana component of the spell's cost is less than three mana. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.