Joshua and I discussed Pythagorean Identities. First, we proved the identities by starting with the Pythagorean theorem and the Unit circle. Then we used reciprocal identities to derive two more Identities. Next we practiced using those identities to perform trig proofs. This was the first time Josh said, "I like it!" in a while! Things have been tough lately, but I think he found some appreciation in the the puzzle-like nature of these problems.