Monday, March 12, 2007

IDENTITIES

MONDAY'S CLASS

Today, we started off class by talking about the calender we have on the blog and what the squared dates mean. Mr. Kuropatwa told us that one of the students had come up to him and talked to him about the math project. The project where each student must generate 4 different equations about what they had learned in the time period. He pointed out that each individual is responsible for choosing a due date for our project. That is why we see different dates marked. If you want to use tools that help you present you work differently like making a movie out of it or doing a slide show, then you should definitely check out studentblogwikitools. The rubric will be made by us. The rubric will be made on Google docs.

He also talked to us about how everyone isn't at the same level and how experts are. Experts don't do problems at their level, they go beyond and push themselves. They never feel like an expert and is constantly not satisfied with where they are. They do problems that they're not comfortable with, but they push themselves.

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1)This is the first equation that we worked on in class. The first slide shows the equation that was given and we had to prove that the right side of the equation was equal to the left side of the equation.

2)Although we see and equal sign does not mean that the right side of the equation is equal to the left side of the equation. So, we treat the equal sign as though it were a question mark because we don't know if they are equal and we can't assume that they are equal.

3)
Ladies and gentlemen, introducing the "Great Wall of China" in math. We use the "wall" because the things on the right side of the sign cannot cross to the left side and vice-versa.

4)As you can see in the fourth slide. The equation on the left hand side can be simplified into 1/ tan²ß + tan²ß/tan²ß.

5)You could also simplify that equation further into cos²ß/sin²ß. That is because tan²ß/tan²ß is equivalent to 1. 1/ tan²ß is equal to 1/ sin²ß/cos²ß, a complex fraction. What you do then is multiply 1/1 by the reciprocal of sin²ß/cos²ß, which is cos²ß/sin²ß.

6)You might have noticed that cos²ß/sin²ß is equivalent to cot²ß. So, you end up with cot²ß + 1.

7)You might have noticed that cot²ß + 1 is equal to csc²ß because it is one of the trigonometric identities that come up a lot.

8)Q.E.D is an acronym, three words in Latin. It's in Latin and is translated to "what was meant to be demonstrated or shown." It's like proven what you wanted to show. Unfortunately, I don't remember exactly what the words are in Latin.

FACT: sometimes in university what may be shown instead of an equal sign is a sign that looks like an equal sign but with another line on top of it. It doesn't mean that this side of the equal REALLY REALLY means that it is equal to the other but it's the same as a question mark where you have to prove that it is equal.


Here are the slides on what we worked on today. Some stuff in the slide is a review from Friday when we first started working on trigonometric identities. There are a couple of new questions on it. We didn't get to go over all of them in class today, but your free to try them. Remember that homework tonight is exercise 15 and I hope this scribe helped. The next scribe for tomorrow is...............................................................................
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MILES!!!

1 comment:

Tim_MATH_y said...

Nice scribe post Sam