Wednesday, March 18, 2009

Trigonometric Identities......BEGIN!!!

Hey guys! It's me, jayp (AKA PJ)! Today we started what seems to be a very exciting unit in our Pre-Cal Class and we also got a little side lesson on the Greek Alphabet!

So starting with the main part of this scribe post, the NEW UNIT! It gives me great honor to be able to introduce to you all, TRIGONOMETRIC IDENTITIES!!!!!
Okay so just in case you didn't get the picture today in class, or you don't get it right now, this picture explains what Trigonometric Identities is all about! So the girl in the picture has many different hairstyles on so she has many different looks or identities, but they are all the same person!


What was shortly explained above is pretty much what this unit is all about! In this unit, we look at the different identities or "looks" trigonometric functions have. This means we aren't exactly solving equations. We are manipulating expressions. As Mr.K put it, we are "algebraically massaging" expressions.


Have I lost you? No worries. Here's what I mean.


In class, we looked at the number 3. How many ways can you write the number three?

Well there's 3.0,
,, and so on. These all look different, but they all mean the same thing. They all mean "3".


Now, because the unit is called "Trigonometric Identities", we will be dealing mainly with the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent). Rather than just plain old numbers, like "3" (Sorry "3").


In class we first talked about how all of the trigonometric functions are made up of two main functions: sine and cosine.

This means,










Now that we had that in mind, we went on to answer some questions from the Smart Board. All of the questions asked us to take an expression which contained multiple trigonometric functions and rewrite them using only the sine and cosine functions and the number "1".
Before you start asking questions about this, yes I made these videos and yes that's me writing things down.

video

Here is a YouTube version if you find this too small!

After these questions, we looked at the Pythagorean Identities! Now this is a little complicated for me to explain here in words (mostly because my head is POUNDING at the moment) so I decided to make a little video!

video
YouTube Version

For some reason the end got cut off. It supposed to say "It can be further reduced to 1."

Now if you didn't get that, feel free to leave me a comment and I, or one of my fellow classmates will be more than happy to answer your question!



Earlier, I talked about how the Trigonometric Identities unit is all about manipulation. It is also about proving things. I'm in a video-making mood so I made a video for this too!

video
YouTube Version

Gotta remember that "Great Wall"!
NOTE: Because you can't put equal signs on the "Great Wall" you cannot solve this as if it were an equation. You must manipulate one side using what you know about identities in order to solve it. (Thanks Anthony for catching that!)
BTW, Q.E.D. stands for Quod Erat Demonstratum which means "
which was to be demonstrated".
Read more here.


We're almost at the end of today! Next we talked about how we could get other identities from what we have just learned! Cue the VI
DEO!!!!

video
YouTube Version
LOL! The music ends early. Darn Movie Maker and laggy computers!!! xD


Tada! This is basically everything we have learned today about Trigonometric Identities! Oh right, about that little mini lesson on the Greek Alphabet. During this unit, many Greek letters will show up. Don't be alarmed with how they look, treat them just like "x" or "theta".

Any who, I was going to make a video about Greek Letters as well but it's getting really late. If you are really interested, wikipedia it or look on the sidebar in the "Equation Maker" thing. The Greek Letters are found under "Characters" and if you hover over them, it tells you their names!



LOL! So I hope you enjoyed my little scribe post with all of the videos. Leave me a comment if they don't work and I promise I will fix them right away!

And now I have the honor of announcing the next scribe! The next scribe is Jessi? Yay Jessi!

P.S. Thanks to jamendo.com for the music! All the music there has a creative commons license so you can use it for free! And the music there is actually pretty good.

5 comments:

  1. now this is exceeding expectations and raising the standard xD

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  2. PJ! we nominate youuuuuuu for the scribe post hall of fame :)

    yes i am two people =D

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  3. Hey PJ, you are the nose to my right eye ;)

    ...and i vote u in as well because your post seems so utterly cool. i hate you for raising up the standards (but love you too <3)

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  4. Hey PJ! I nominate you for the hall of fame because videos are a very creative and effective way to teach the students in our class about the subject. ;)

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  5. i choose you pj!

    i nominate pj's scribe for the hall of fame because of his very engaging post.

    ReplyDelete