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Tuesday, March 14, 2006

lucky scribe # 24

Happy π day and happy coin hunting everyone!

So today we had a two period day but it wasn't just an ordinary day. In our morning class we started off with two identity questions right away:

cos ø ∙ csc ø and sec² α-1

As we were doing these questions Mr. K give us a few sets of guidelines:
  1. start with the more complicated side, meaning the side with more variables
  2. rewrite everything with sin and cos
  3. always look fPythagoreanean related identities
  4. make a complicated equation simpler, not more complicated
  5. simplify as much as possible *e.g. compress different fractions into one fraction
  6. and you can always "rewind erase", make different choices nothing is engraved in stone.
*NOTE: These are not rules! There are no rules to solving identities! These are just guidelines!!!
And this is how one would solve these questions, but just remember that there are many many ways to solve identities.

cos ø ∙ sin ø
= (cos ø/1) ∙ (1/sin ø)
= (cos ø/sin ø)
= cot ø

sec² α -1
= (sec α -1) ∙ (sec α +1)
= ((1- cos α)/cos α) ∙ ((1+ cos α)/cos α)
= tan² α

So the rest of the period we were given more identity questions and did a lot of practice because that's the only way you'll get better on solving identities. In most of the questions given we had to use the Pythagorean identities. There are only three Pythagorean identities that you have to remember:

sin² ø + cos² ø = 1
1+ cot² ø = csc² ø
tan² ø +1 = sec² ø

Then from the three Pythagorean identities you can derive corollaries by balancing the equations.

For example from sin² ø + cos² ø = 1, you can derive two other identities:

sin² ø = 1- cos² ø and cos² ø = 1- sin² ø

Then in the afternoon class we celebrated π day!!! YEA!! Everyone brought pie, it was so awesome! We ate pie, LOTS and LOTS of pie with a good variety of flavors from apple, rhubarb, pumpkin, apple cranberry, blueberry, chocolate cream and coconut? cream? pie?!? Hmmmmm I probably ate 5-6 different slices of pie that were cut IN RADIANS.

Okay so we celebrated a little too early so at this point when everyone had their share of pie we did some math before π time. And in the spirit of π we did identity equations where 0 ≥ ø ≤ 2π we solved the equations graphically using our calcualtor and algebraically. Then we did a countdown 10 seconds before the official π time and on 1:59:26 everyone in class all together screamed "Pi!!!" while holding a piece of pie and stuffing it down our throats after. Ahhhhh π day... I'll miss you.

Thanks to everyone who brought pie, drinks, cutlery and anyone else who contributed to our π day celebration. Now do your homework, please.
pg. 264, odds, #'s 11-35
..and the next scribe is MARK.

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