We have a similar story with introducing our pit (Madison) to our cat Sherlock. I agree with everything that is stated above, ESPECIALLY about the dog being exercised before dog/cat interaction.
Just a caution however, Sherlock (and most cats in general)is a little instigator!! He will initiate chase by running up to Madison, and as soon as he approaches her, runs the other way! She, for the most part does well. However, if she hasn’t been exercised enough she will ensue in the chase game.
For the most part, they now play with Sherlock flipping onto his back while Madison nuzzles her snout in his belly. He will shrimp off her face and move his body a bit, then she’ll place her snout in his belly again. She has learned to become very gentle with him, despite the fact that he is not declawed and I am not the best at keeping up with his soft paws (a bit ashamed of that). It is very cute to see the two of them play. I will probably ended up posting a video of it in the near future 🙂