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Tuesday, February 14, 2006

Functions of Sin and Cos

Happy Valentines to all!! Sorry that this blog is just being posted now. I was having technical difficulties trying to figure this create the blog process. Unfortunately i was chosen to be the scribe when we had two classes. THANKS Emile. Just kidding and anyways let's get started with this blog.


Today we had two periods of math. Mr.k talked to us about PI Day. This special day occurs on March 14 at 1:59 and 26 sec. in the afternoon. Coincidently, it's the best time to eat pie.Mmmm. Also he told us about the coin hunt also happening on the same day. That was very funny how those teachers cheated their way into winning the hunt. Another event that was going to be going on is the math Carnival when the jr. high's come for their tours.

Today in class, we went over sine and cosine functions. The diagram below shows how each functions looks like.

For Sin,


For Cos,


The equation of the function is as follows: y= AsinB(x-C)+D


We only learned what D and A do to a graph. D is the sinusoidal axis or vertical shift or the average value of the function. Therefore, whatever the number substituted for D, it will be the y-coordinate of the imaginary line in which the function wraps around to. For example, if D was 1, the graph would like the diagram below.

In this diagram, the sinusoidal axis is at 1. Therefore it moved the function one unit higher.


Nextly, we looked at what A did to the function. We learned that A changes the amplitude of the function. In other words, the distance between the maximum or minimum of the function and the sinusoidal axis has changed. For example, if we were given the function, y=2cos(x), the diagram would look like the one below.

Lastly, Mr.K went over with us on what B does to the function. By plugging the information, y=sin(2X) into our graphing calculators, we saw that there were more waves in a given domain. In this case, there are 2 periods in the interval 2π. The diagram below will show the function
y= sin(2X).

The formula for finding the period of the function when given the equation is:

period = 2π/B

There is a short cut to drawing sin or cos functions when given a B value. Instead of drawing all those periods in the given interval, you can draw it like your basic function and just change the radians on the x-axis. The diagram below will give you a better understanding.


For the people who missed today's class, here's your notes. Finally I'm done!!! Hope you guys liked it.*YOU SHOULD, I PUT 2+ HOURS OF HARD WORK* Anyways. I have the honors of choosing our next scribe, who is........................................................................................................................................

........................................................................................................................................................................

.............................................................................................................................................Janet.


ps. Thanks Mr.K and Jackie for the help!!




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3 Comments:

At 2/15/2006 9:11 AM, Blogger Mr. Kuropatwa said...

Mike, what an awesome scribe post! Outstanding graphics! The best one was the last one where you showed how to sketch the graph for changing values of B by relabeling the x-axis.

You have raised the art of scribing to a new level. Simply fantastic!

 
At 2/15/2006 9:59 PM, Blogger mark said...

very colorful, and more will be expected from the next scribes.

 
At 3/01/2006 5:35 PM, Blogger Regine said...

this is a late comment, but good gosh darn job. hahaha. Your scribe was articulate and your graphs are fabulous.haha.that's right. FABULOUS

 

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