Thursday, September 6, 2007

FIRST SCRIBE POST ! " UNIT CIRCLE "

ALRIGHT-Y FOLKS ! Sorry about having the post really late, but I hope there isn't an exact deadline yet for posting the blogs ! Anyways, today's math class all began with Mr. K finishing off where he had started from yesterday, and quickly finished off with the slides he was showing to the class about being in class on time and habits, and etc. Now, this is the time where Mr. K pops up a question which leads into what we learned today, the question was:

Why are there 360 degrees in a circle?

Now, I know what you're thinking, you're probably going " EHHHH !?? " I know I did, because Mr. K surprises you =P.

Some people must have had answers but were sh
y to shout it out, but I myself was not able to come up with an answer to my head, however there was this one answers which was quite interesting, and the person had commented that it was related to the calendar and made a very interesting comparison, however it was so interesting I can't explain it myself, but I knew what he said. Unfortunately that wasn't the answer Mr. K was looking for, but it was a very good answer props to that guy, it blew my own mind away. Now, back to the topic about calendars, Mr. K mentioned an interesting fact about how the deck of cards represents a calendar, that was cool.

Getting back to the question
Why are there 360 degrees in a circle? Mr. K led us to the answer by asking us if 360 was divisible by all the numbers we could think of. We came up with

1,2,3,4,5,6,8,9,10,13,15,20,24,30,36,44,45,60,72,90,
120,180,360. These are a lot of numbers ! So therefore, from that, the answer was, that 360 is the number of degrees in a circle because it cut into evenly pieces.

Mr. K had then given us some math questions to do.
1. x/4.5 = 7/9
2. 4/x = 13/
π
3.
π/8 = x/180
4. 31/50 = π/x

To make life easier, here are the answers: *REMEMBER, IF ANSWERS ARE IN THE DECIMALS, THEY SHOULD BE IN THE 4th PLACE, AND HE HAS HEARD YOU SAY THAT YOU HAVE ALL HEARD IT, DO NOT FORGET! =).

1. x/4.5 = 7/9
x = 4.5(7)/9
x = 3.5

2. 4/x = 13/π
x = 4π /13
x = 0.9666

3. π/8 = x/180
x = 180π/8
x = 70.6858

4. 31/50 = π/x
x = 50π/31
x = 5.0671

Those are all the answers for the questions that were in red. Also, these questions, do not need to be answered in decimal approximation, but rather in an "exact fraction."

For example, 4/x = 13/
π => 4π/13


Later on, Mr. K introduced the class to the "Unit Circle"




That is the unit circle filled with all the radian measures around the circle, looks confusing, but it isn't really, if you try to look at it closer ! Mr. K will teach us more about it in later classes, or better yet, ask him about it on your free time, and also on his free time, for better understanding of the unit circle, and DON'T BE SCARED ! Or else ! you'll never learn, if you don't ask QUESTIONS !

This diagram is of the Unit Circle has measurements in degrees.

Shortly after Mr. K introduced this he then gave us the question:
Convert 20° into radians.

20
°/180° = θ/π
= 20
π = 180(θ) = 20π/180 = θ
= π/9 = θ

Then
he also showed us how to convert radians into degrees.
Convert
π/5 into degrees.

θ/180 = π/5 / π ( this is called " complex fraction )
= θ/180 = (π/5)(1/π)
= 5
θ = 180
=
θ = 180/5
=
θ = 36°

We basically, learned how to convert degrees and radians
, this is the equation given at the end of class.

D(angle in degrees) / 180
° = R(angle in radians) / π

Alas, this is at the end of my scribe post, and I hope you've all enjoyed reading, and study hard everyone. Before I forget, these are the two Phrases you'll hear a lot during this semester of Mr. K's math class.

"Fractions are our friends" "Mathematics is a science of patterns"

remember them well, and you'll DO well in the class, and of course asking questions and studying and forming groups with people you do not know ;).


TUNE IN FOR NEXT CLASS ! A story of a guy who died because of a triangle, dun dun dunnnnn ......

1 comment:

SAMUS said...

good job oliver (y)
good scribe.