Including inverse trigonometry with the Law of Sines and the Law of Cosines may seem like a weird pairing, but there are a few reasons why I felt that it made sense. From a purely practical standpoint, I wanted to do a “No-Calculator” assessment for the circular trig unit, but I wanted the students to be able to use their calculator to solve problems involving geometric trig as well as for solving equations involving inverse trig, so grouping the topics in this way was a good match for my assessment plans. Furthermore, the ideas of equation solving with inverse trig arise naturally when solving geometric trig problems, especially when students are using the Law of Sines to find an obtuse angle. But that being said, the material from this unit on inverse trig could easily be moved to the unit on circular trig.
This is only a partial unit. The reason for this is that there are already plenty of good problems on Law of Sines and Law of Cosines. (I particularly like the problems in Richard Brown’s classic text Advanced Mathematics.) For that reason, I’ve primarily concentrated one developing the intuition for these formulas instead of writing tons of practice problems. As always, enjoy!