Day 7 in MAT229

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Today: Inverse Trig functions
- Your assignments and schedule are complete for the week.
- You have a lab due Saturday by midnight, and then a small flurry of assignments to hand in next week. I hope that you're making good progress on the weekly assignments.
- A reminder that our first exam is coming up: not this weekend, but the next weekend. You'll have several days over which you can take it, but it will be by lockdown browser (and probably a couple of IMath problems).
  It's going to be a recap of some problems from Calc I, with a new collection of functions (these exponentials, and inverse functions).
- Today we're looking at inverse trig functions.
  Trig functions are terribly important, for handling periodic phenomena (cyclical phenomena -- e.g. the number of hours of daylight over the course of the year(s); cicada outbreaks; migrations; spinning of a top; current in a transmission line; your heartrate; etc.).
  These functions are not one-to-one, and so you might think that we need to throw up our hands and say "Forget it!" Well
  
  "Hah!"
  We're not that easily shot down.... We simply do what you've done for years and years and years with square roots:
  
  What's the square root of 4
  Most of us say "2". Some of you will say "$\pm 2$, and some obstinate ones among you may just say "-2". :)
  It's all about domain restrictions. That's going to be the key.
- Once again, we'll see a connection between the derivatives of these inverse trig functions and other classes of functions. In particular, the inverse tangent gives us an anti-derivative for the function \[ \frac{1}{1+x^2} \]
- Materials:
  - Inverse Trig Functions (.nb)
  - Inverse Trig Functions (.pdf)
  - Long yacks through the notes using Mathematica:
    - Part A
    - Part B

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