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Monday, May 15, 2006 

Scribe ; Periodic Functions

Hello everyone =] So today we only had one class but we also started our next unit: Periodic Functions (circular functions). Mr. K started off the class by asking; Why are there 360° in a circle? After much discussion, we answered (Nick in particular) that it was because it can be divided evenly by many numbers:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

But Mr. K also showed that the initially, the military put 400 gradiens into a circle. Most likely, they wanted 400 gradiens because 100° could be set per quarter. Although 400 can be divided evenly as well:
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
..360 can be divided by many more numbers.

But another question was presented: Is there a natural way of measuring angles in a circle? And the answer being Radians. Mr. K showed on the board that the number of times that the radius will fit in a half circle is exactly π. And if you go around the whole circle, the radius will fit into it 2 π times. Radians have no unit, there's no particular 'measurement'. Here's a picture of what a circle would look like divided into radians.



As shown above, we can convert degrees into radians. Thus, radians is the natural way of measuring a circle. After we learned this, we tried a few simple problems that just dealt with converting degrees into radians: (making sure to show every step possible..)

40°/180° = θ/π
θ180/180 = 40π/180
θ = 2π/9

And then we started talking about how you can solve triangles from within the unit circle by using the pythagoreom theorem.



Also, when using the unit circle, the radius will always be 1, always. By the way; Pythagorous was incredibly ugly and thought that beans had souls..very interesting. haha. Anyway, back to math. You can actually convert that to a sinusoidal graph:



Also called a sine wave. Any graph that repeats = periodic. Which is exactly what this wave is (2π is the period). The period is described as the number of times it takes to repeat. This consists of a minimum, maximum and average. Also, it never goes past the max and under the min.

And thaaaat boys and girls was today's class ;) Oh and, tonight's homework is on page 216, number 1 to 7.

The scribe for tomorrow is R-E-I-G-N *have fuuuun!*




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I've thought long and hard about it. This post belongs in The Scribe Post Hall Of Fame.

The colour and graphics so clearly illusutrate what you've written. I must have refered to this post of yours in class every day since you posted it. You've made it so easy to understand the material.

Well done! And congratulations. ;-)

Hi Stephanie,

Congratulations on your induction in the Scribe Post Hall of Fame!!

Explaining complex concepts in a way that makes it easy to understand is often very difficult, often impossible for many. Perhaps teaching is in your future?!

Best,
Lani

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