Thursday, March 19, 2009

Yay Identities!!!!!

Hey everyone

Well to start off class today, Mr.K wanted to talk about the "Blogger Hall Of FAME!!". We took a few votes on the subject and here's what we decided:

1) It takes a MINIMUM of 12 votes to get your blog into the blogger hall of fame.

2) NO anonymous votes.

3) NO voting for yourself.

Once we were done with our little bit of classroom democracy, we split up into groups to work on some practice problems. Once we were in our groups, we did a little recap on Pythagorean identities. Remember:

eq=sin^2\theta +cos^2\theta =1

As practice, we simplified a few simple expressions using Pythagorean identities when we could.

Example #1

eq=csc^2 t - cot^2 t

1) first change the expression to only use sine, cosine, or 1

eq=\frac{1}{sin^2 t } - \frac{cos^2 t }{sin^2 t }

2) this leaves you with two fractions with the same denominator. Rewrite the expression

eq=\frac{1- cos^2 t }{sin^2 t }

3) since the numerator is a pythagorean identity, we now know that the numerator is equal to sin^2 t

eq=\frac{sin^2 t  }{sin^2 t }

4) the numerator and denominator can be factored and the answer that is left over is 1

Once we had finished simplifying the expressions, we found that two of the expressions simplified to the same thing, in this case 1. We used them to write the equation

To check if this is true there are a few strategies that we could use. These are:

1) Work with the more complicated side of the identity first

2) Rewrite both sides using sine and cosine

3) Use a Pythagorean identity

4) Simplify complex fractions or rewrite them

5) Use factoring (especially to create differences of squares)

A very important thing to remember when proving trigonometric identities is that you have to drop down "The Great Wall of China" and you can NOT cross it. This is because, when proving an equation, there is no way of knowing whether or not it is true.

So now that we have covered proving trigonometric identities, on to a new subject!!


sin(-x)=-sinx cos(-x)=cos(x) tan(-x)=tan(x)

the sine and tangent functions and ODD functions

cosine is an EVEN function

ok so now i've gone through pretty much the entire class of today. There is only one more thing from class that i must remind you of:
so i'd bring something comfy to wear. Mr.K said that as soon as you get into the room get into groups of four, with at least one person in your group that you have NEVER worked with.

One last thing. The scribe for tommorow is..... YI NAN!!!! =D


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