Today:
- Announcements:
- Exams are graded. The distribution was fairly normal, but I'll add a few points to push a few folks over into the A column (and move everyone up a bit, of course).
- Mean: 75.5
- Curve: Add 3 to the score at the top of your paper.
- Check my addition!
- I saw some really great stuff!
- I saw some really scary stuff!
- We'll take a look at both. The good stuff I'll highlight
in the key, which is made up of your
good solutions.
- Let me say something about the scary, sad stuff. There
were four things, especially:
- I thought that I'd telegraphed the importance of
the limit definition of the derivative (but who
knows what a telegraph is anymore?).
- Algebra can save you, or you can drown without it.
- Compositions aren't well enough understood (with
implications for limit definition, chain rule,
etc.).
- Symmetry, symmetry, symmetry -- another way to
save yourself.
I'll point each one out as we look over the key, and point out a lot of the
very good things too!
- Small (but very important) thing: in calculus, make sure
that you're in radian mode for trig functions.
- Today we will also finish up section 7.2: Trigonometric Integrals
- We're hopefully recognizing the utility of trigonometric
identities.
- There are really only three that are 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:
\[
\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\beta)\sin(\alpha)
\]
- So let's have a look at our handout for 7.2.
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