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Thursday, February 09, 2006

Scribe #4: Circular Functions

Beautiful day, beautiful day, here in Winterpeg, Manisnowba. This is Manny doing the scribe for today! I'll try to make this as short and concise as possible, because I'm just a straight to the point kind of guy. Well let's get down to it then.

Today in class we got a surprise, quiz on circular functions (out of 16 marks). It wasn't too bad, there was nothing new, it was just the stuff we've been doing all week long.

The quiz consisted of 4 parts:
Convert to Radians
2) Convert to Degrees
3) Determine the Quadrant of a Radian given
4) Determining a coordinate on the unit circle given a coordinate outside the unit circle.

The toughest part of the quiz that a lot of people had difficulties on was the last part. The question went like…

“Assuming the point P lies on the intersection of the unit circle and the line segment joining the origin to the point Q(-9, 40) find coordinates of P.”

Here’s how what the diagram might look like if you were to draw it:

Well, how I tackled the question was stating what I know.
- On the unit circle, the radius, which is the hypotenuse in this case is always equal to 1.
- The coordinate Q(-9,40), is expressed as (cosine, sine), because cosine runs along the x-axis (horizontal distance), and sine runs along the y-axis (vertical distance).

Therefore, cosine = -9 and your sine = 40.

So you now need to find your hypotenuse, and when you find your hypotenuse you can reduce that value to one by dividing whatever number it may be with itself. When you do that, you must divide your cosine, and sine by the same number of what the hypotenuse was in order to not change the value of anything.

With the Pythagorean Theorem you can find your hypotenuse because it is a right angle triangle.
h² = cos² + sine² where h is your hypotenuse
h² = -9² + 40²
h² = 81 + 1600
h² = 1681
h = 41

So by dividing the hypotenuse by itself will get you the value of 1 which is on the unit circle, and you must now divide all other values by the same number in order for it to remain the same value.

So on the unit circle, cosine = -9/41 and sine = 40/41
Therefore the coordinate would be P(-9/41, 40/41)

During the quiz to those who were done, Mr.K wrote up some brain stumpers (well to me anyway) on the white board to pass the time. I’m usually bad with puzzles, I only got the first one =(. It kind of looked like this.

Can you draw these pictures without lifting your pencil and crossing any line?

Well back on topic, after everyone was done the quiz, we switched papers and marked. Apparently there are many provincial rules on marking, which can cost you many marks and which applies to us.

Some of the rules I remembered are:
- always reduce to lowest terms
- don’t have a train of “=“ signs
- follow what the question says, e.g. round of to nearest tenth, so if it was 3.43, it would be 3.4, not 3.43
- make sure you have the variable in which the answer is equal to, don’t just drop it (I have a tendency to do this one), e.g.
x= 10/2
= 5
(wrong) x = 5 (right)

These are a few mistakes we tend to make by not following certain rules, and from now on it’ll cost us marks! So always be on the look out for these little mistakes.

Then we went over some problems that some of us had difficulties on, in our homework assignments. And then it was the end of class. Whew… I tried making it as short as it could be, but it seems like I can go on and on. Sorry if none of it made sense to anyone. If it didn’t you can ask me to explain it to you in person anytime, and I’ll try my best to. And no homework for today! So celebrate while you still can.

Oh and, if anyone has a few ideas or suggestions on how to convince Mr.K to let me move from the front row seat to anywhere else, let me know and I’ll give you candy =). Like Sisyphus I’ll never give up. It’s just too bad Mr.K has the same attitude. But he’s playing more a role of Hades in this case scenario, where he’s putting me in a spot for like forever and will never let me leave from it. *Sigh...

Well it’s been fun being the scribe for today, now, next on my list of priorities… food.

And, I almost forgot! The next scribe is Jacky S. Why? Just because I can…=D

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At 2/09/2006 7:32 PM, Blogger Van said...

I like the way the scribe keeps getting longer and longer everytime. Even when today wasn't even a busy day.

At 2/09/2006 8:19 PM, Blogger Jefferson said...

I agree

At 2/09/2006 9:41 PM, Blogger Darren Kuropatwa said...

Outstanding scribe post Sisyphus ... uh ... I mean, Manny! ;-)

I really liked your use of colour and the graphics you used.

One thing; you have a line that reads:
Therefore, cosine = -9 and your sine = 40

Cosine is related to a measurement on the x-axis, it is not the same thing as any measurement along the x-axis such as -9. It is the same as a measurement on the x-axis only in the unit circle. A better way of describing the situation in the problem would be to say: "The adjacent side is -9 and the opposite side is 40 in the large right triangle defined by the the origin, x-axis and the point (-9, 40).

Your post has really set a new standard for all the scribes that follow you. Way to go!

Hades out. ;-)

At 2/09/2006 10:11 PM, Blogger Emile said...

Thank God Manny, it wasn't me you choose.A job well done....!!!!


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