I have 3 more pills of bactrim (sulfamethoxazole and trimethoprim) to take - how long until my coc (yaz) is fully effective again? should i use a secondary method of contraception?

Yes: Trimethoprim, one of the ingredients in bactrim (sulfamethoxazole and trimethoprim), (sulfamethoxazole and trimethoprim) mildly induces the liver to process the hormones in birth control pills faster, theoretically reducing their effectiveness. The half life of bactrim (sulfamethoxazole and trimethoprim) is only 8-10 hours but the enzymes that are induced take longer to return to normal levels. The usual recommendation is to use a backup method for 7 days after finishing bactrim (sulfamethoxazole and trimethoprim).