- Your assignment over 6.3 is due.
- Note: the old syllabus had "6.7" listed next, rather than 6.6 (inverse trig functions). So I've changed the syllabus. Today we study inverse trig functions.
- I found some study materials from our textbook's author, and have made a sample available on-line. You might try the chapter 6 materials.
- Your quiz opportunity tomorrow will be over section 6.8 -- L'Hopital's rule. Please read ahead!
- The first place to start is the geometric perspective, perhaps.
As usual, we're focused on the undoing property: if the question for us begins as "What is sine of 30 degrees?", the undoing question is "Whose sine is
?"
We should immediately observe that the original question has a unique solution, whereas the "undoing question" does not. Because sine is not one-to-one, we shouldn't be surprised. But this is an issue: how do we create a useful "inverse" of a non-invertible function?
- Well, we need to worry in particular about three cases: sine,
cosine, and tangent (the others -- secant, etc. -- I don't really worry
about too much, but they do sometimes come into play):
- Two of these inverse functions are shown in their entirety; the other isn't. Which is which?
- What features of a graph would have helped us to identify these more easily?
- The graphical definitions of these functions are easy, carried out
via the mirror. But what are the properties of these inverses?
For example, what are their derivatives? These we've carried out before, using the amazing rule for inverse functions -- do you remember it?
- Let's look at a few problems involving these curious inverse
functions:
- 1, p. 459
- 6
- 14
- 18, p. 460
- 22
- 48
- 49