Problem Set 6

For Thursday, Mar. 17

Problems

1. Write up the derivations of your four identities from the conjunction/disjunction theorems applied to the Menelaus configurations that we did in class today. These should include proper pictures and complete arguments (enough to be readable if you put them away in a drawer for a year and looked at them newly then).
2. Translate those four derivations into a set of identities using the modern notation for a spherical right triangle, with vertices (and hence angles) A, B, C, and opposite edges a, b, c, where c is the hypotenuse. Note there are two possible triangles depending on where you put a and b, and you want to apply your four trig identities from #1 to both configurations. (We started this in class today.)
3. For each of the identities you generate above, identify which of the ten fundamental identities on page 79 your identity corresponds (e.g. the second identity on list II can be denoted II.2). The big question: how many identities are accounted for by your derivations?

When turning in Problems 1-3 above, please write neatly and take pride in your presentation.