Day 15 in MAT229

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Announcements:
- Ironically I posted the a version of Lab 4 including the Mathematica solutions, so let me pretend that I actually intended to, and that the point is that you are to get the same answers (roughly) by hand! (Can you all pretend that?)
  One caveat there: I usually do the lab keys, and Prof. Wilkinson and I go back and forth, to get it the way we like it. So I don't know if the version I put up corresponds to the actual lab we intended. So I'll put that one up, just for reference.
- Week 4. Remember we didn't have a weekly assignment week 3, because of the exam; Hence, this week we encounter weekly Assignment #3: due Monday, 2/8
  (here it is as a .nb)
Today we begin a section on trig integrals.
- We'll look at a few examples which illustrate the importance of trigonometric identities.
- We'll also look at some of the useful identities that we'll want to use from time to time. The good news is that only three are really essential (and you can get two of them using texpand on your TI calculator). You can derive the rest from these three:
  - The trig form of the Pythagorean Theorem: \[ \sin^2(\theta) + \cos^2(\theta) = 1 \]
  - Sine of a sum: \[ \sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha) \]
  - Cosine of a sum: \[ \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\beta)\sin(\alpha) \]
- Here are our materials for today:
Links:
- Wolfram's Alpha is sometimes pretty helpful.

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