6th Scribe Post: Quiz 1 on Circular Functions

Hi everybody!! I'm Ashley and I'm the scribe for today's blog! At the very beginning of class there wasn't much talk about math which is a good thing for me. I don't have to write down as much. Mr.K basically said from what I heard is that you should not reveal personal information on the internet. He stresses no last name should be shared and that we should read the post "Student's made this" because it's very important. Another thing he said was that to post a blog you should go to beta.blogger.com and sign in there to post. So after he went on about the blog he revealed that there will be a quiz. I was in complete shock but then I remembered him saying that yesterday so it wasn't a total surprise.
The quiz was called Quiz 1 on Circular Functions and these are the questions(blue) and answers(red):

1) Convert the following to radian measure, expressing your answer in terms of Π. (2 marks each)

(a) 25°
180°/Π = 25°/θ
180θ = 25Π
180θ/180 = 25Π/180
θ = 25Π/180
θ = 5Π/36

(b) 460°
180°/Π = 460°/θ
180θ = 460Π
180θ/180 = 460Π/180
θ = 460Π/180
θ = 23Π/9
*Remember to add the degrees symbol on your setup because you will lose marks. I think it's -.5 for this question.

2) Convert the following from radain to degree measure. Round your answers to one decimal place where necessary. (2 marks)

(a) -7Π/6
180 º/ Π = θ /-7p/6
-659.7345 = θΠ
-659.7345/Π = θ/Π
-210º = θ

(b) 2.634
180 º/ Π = θ/2.634
474.12 = θΠ
474.12/Π = θ/Π
150.9º = θ
*Remember like in the first question to add the degrees symbol on your setup because you will lose marks. I think it's -.5 for this question as well.

3) Determine the quadrant in which each angle lies. (1 mark each)

(a) 2Π/3

Answer: Quad II

(b) 11Π/6

Answer: Quad IV

(c) -Π/4

Answer: Quad IV

(d) -11Π/6

Answer: Quad I

4) 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 the coordinates of P. (4 marks)

(-9)2 +(40)2 = r2

81 + 1600 = root of 1681

root of 1681 = 41

x/-9 = 1/41 => x = -9/41

y/40 = 1/41 => y = 40/41

Sinθ = 40/41
Cosθ = -9/41
P θ = (-9/41,40/41)
*Remember if you draw a diagram you must correctly place the angle in the right place on the circle. For this question you would have lost 1 mark. Another thing is to add the equal sign where needed because you will lose marks and to correctly place the x and y coordinates in the answer.

After the quiz he collected it and randomly gave us other people's quizes. He told us how to correct it and where we would lose the marks.
You would lose marks in the following:
- Not adding the degrees symbol
- Incorrectly placing an angle on a diagram
- Not placing the equal sign on your work
- Incorrectly placing the x and y coordinates in the answer for example if the answer was Pθ=(9,40) but you put Pθ = (40,9).
There's more but I can't remember them but you get the idea right? The setup should always be correct because it's not only about the answer but the steps you take to get to the answer is important too.

I'm not done yet so bare with me. Just before the bell rang Mr.K wrote on the board
5x - 3 = 4x + 16
5tanx - 3 = 4tanx + 16
tanx = 19
He then told us we were looking for the arc tangent of 19 and told us to punch in 2nd function tangent then 19 into our calculators. The answer became 86.7º which we round off to 87º. We know that 87º is in quadrant one but wait there's a second answer as well.
Remember that sinθ maximum is -1 and 1 and cosθ maximum is -1 and 1 as well but tanθ has no maximum. So there will always be two answers. To find the second answer remember that in Quadrant I, tanθ is positive but in Quadrant III tanθ is positive as well. So you would have to add 87º after Quad II which will look like this:
87º + 180º = 267º which brings you to Quad III.

So that's it for me. Yay! If there are any mistakes please comment okay because I'm still new to this and this is my first post. Bye for now!

Oh by the way the next scribe will be........ hellochipsahoy

Scribe Post 5-- Reciprocals of Trig functions etc

Second Scribe Post

Yeah this post has been really late, you see first time I had problems even signing into the site it's been fixed now, I just forgot.....then had to be reminded.

Don't expect too much, just an early warning.

The start of the class was about the same as usual we began with a quick
set of questions on the board then we went over them and the homework that
was assigned to see if anyone needed any help.

During the lesson one of the subjects was about how negative degrees moved in the opposite direction (clockwise) compared

to the positive which moved counter-clockwise.

Aside from that we also talked about using radians to figure out which quadrant it was indicating.

For example -8π/45, since -8 the numerator isn’t half of 45 the denominator the angle remains in quadrant four rather then quadrant 3.

Another example would be 5/9, one might assume otherwise but since the numerator doesn’t have the π symbol the numerator is actually less then the denominator.

Lastly we went over the equations for calculating arc length and areas of sectors along with converting degrees and radians.

Converting Degrees & Radians:

[π/180° = R/D] R = Radians can also be written as [D/180° = R/π]
D = Degrees

Calculating Arc Length

[θ/360° = Arc Length/2πr] r = radius


Calculating Areas of Sectors

Angle out of 360°{θ/360° = Sector/π r2} Sector out of the total area.

Short ain't it?
The next scribe was already informed a long while ago.

SCRIBE # 1 !?, intro to circular functions

GREATINGS!! FELLOW STUDENTS! Jefferson is the scribe for today.
Mr K started us off with a one billion dollar question, why does a circle have 360 degrees? Well one classmate said that in ancient times back when there were Babylonians, they had numbers with a base of 60. We count numbers with a base of 10 mind you. Their calendar had 360 days in a year, and one full cycle (sun orbiting around our planet) would take 360 days. Mr K agreed, however he said that there was another reason for why a circle had 360 degrees. He then asked if we could use a different number instead of 360. Christine said 100 because it was easier to use. Mr K said that the British liked Christine’s idea so much, that they actually used it. Instead of degrees, the British called it; “gradians” .There was actually 400 gradians in a circle instead of 100 gradians. Mr K then asked us a really tough question. Why is 360 degrees in a circle? Wooo, what a toughie. Mr K asked us what the factors of 360 are. We then regurgitated , “ 1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,72,90,120,180,360. Mr K then asked, “What are the factors of 400? “ We the regurgitated, “1, 2, 3, 5, 8, 10...etc” Mr K said that 360 is evenly cut up using more number(factors) than 400 (which lead to the fall of gradians, you said it folks, gradians didn’t catch on)
Now acting like a magician, Mr K asked for a volunteer. What trick does Mr. K have up his sleeve? Let’s find out shall we? Jessica volunteered to be the guinea pig- volunteer. MR told Jessica to spread her fingers as far apart as possible and place her thumb and pinkie onto a circle/graph that Mr. k drew during his lecture. Jessica gets her own measurement from the space from her thumb to pinkie called “Jessica” units. He then took a towel and placed it from the center of the circle to the circumference. He explained that the towel represented the radius of the circle. He then rapped the towel around the half of the circle. He said that the measurement was indeed NOT Jessicas, but RADIANS. The number of towels that took to be wrapped around half of a circle was 3 and a bit. That total length is none other than PI!!! And I’m not talking about the desert. A rough definition for pi is a measurement was formed from wrapping the radius around half a circle 3.14 times. And again Mr K asked us another hard to find answer. “Why are there 2 triangles in a geometry set” half of us never even thought about it. Well. The first triangle, the isosceles (triangle that has sides of the same length)/ right triangle, has 45 degrees in it. And the other triangle had a 30 and 60 degrees in it. 30,45 and 60degrees are the angle measurements that are used the most. On the unit circle 30 degrees are broken into sixths, 45 degrees into quarters, and 60 degrees in to thirds.




the red numbers (45 degrees and so on) brake up the unit circle into quarters

the green numbers ( 30 degrees and so on) brake up the unit circle into sixth

the blue numbers (60 degrees and so on) brake up the unit circle into thirds

here's the unit circle in radians

Now where did those triangles(from our geometry set) come from? It pretty much came from the unit circle. 45 degrees is pi/4.

How do we convert degrees into radians you ask? Well its simple, follow this guideline : 180º/Π = D / Θ. This translates to : 180 degrees is to pi the same way to an angle is to radians.

Mr k then gave us a practise problem to do:

What is 40 degrees in radians?
*remember to follow the guideline

180º/Π = D / Θ
180º/Π = 40 º/ Θ
180Θ = 40Π
Θ = 40Π/180
Θ = 2Π/9

Here’s another one:

What is 50 º in radians?

180º/Π = D / Θ
180º/Π = 50/ Θ
180Θ = 50Π
Θ = 50Π/180
Theta = 5Π /18

What is 2 radians in degrees?
180º/Π = Π /2
360/Π = (ΠΘ)/Π
114.592 º = Θ

And thus ends our scribe post- NO WAIT THAT WAS ONLY THE FIRST CLASS, WE HAD TO CLASSES TODAY!!

In our second class, Mr. K attacked(don’t mean literally) us with math problems on the white board. >

Convert to radians

A) 25 º

b) 260 º

A)
180 º / Π= 25 º/ Θ
25Π/180 = Θ
5Π/36 = Θ

b)
180 º / Π = 260 º / Θ
260Π/180 = Θ
13Π/9 = Θ

Convert to degrees

A) 4.5

b) 12Π/5

A)
180 º/ Π = Θ / 4.5
810/Π = Θ
257.831 º = Θ

B)
180/Π = Θ/ (2Π/5)
2160Π/5 = Π(Θ)
432 = Θ

Find the indicated angles:

a)

A = 75 º since angle a is opposite of 75 ºthen angle a = 75 ºbecause they are both opposite angles

b)

A = 70 *angle a and 70 º are both alternate angles so the equal
C = 180 - a
C = 180 - 70
C = 110
B = 180 - 70
B = 110

* angle b is congruent with 70 degrees

c) find the complement of 50 degrees

90º- 50º = 40 º

*compliment is and angle whose sum adds up to 90 º

d) find the complement of pi./ 3

Π/2 - Π/3 = 3Π/6 - 2Π/6

Π/2 - Π/3 = Π/6

*”complement is and angle whose sum adds up to 90 degrees” 90 degrees in radians is pi/2

E)find the supplement of 15 º

180 - 15 = 165

* supplement is an angle whose sum adds up to 180 º

F) find the supplement of Π/4

Pi=Π/4 = 4Π/4 - Π/4
Pi - Π/4 = 3Π/4

Mr K then gave us a brief explanation about the right triangle and the Pythagorean theorem
Pythagoras was a Greek man who was famed for being very intelligent, unfortunately he was super ugly according to Mr. K
He drew 3 different sized right triangles and asked us how they are the same?
He then referred to something that we’ve learnt back in grade 9: soh cah toa. Which means sin = opp/hyp, cos = adj/hyp, and tan = opp/adj.
He then made us take out our calculators and challenged us to a race. Mr k will give us an angle to input into our calculator sine of 50. Well out 4 questions, it seemed that Mr. k had the upper hand even though he used his head to calculate the answers instead of using a calculator. The answers where all the same too : .5 and -.5 where the answers to the questions
He said that all the right triangles ended up with the same answer because they are virtually the same but in different sizes. He can shrink on down as small as possible and come up with an answer that is 0.5 and blow another triangle up and it would still be the same answer.

you may wonder what this triangle thing means. if you compress triangle as small as possible the hyp. will have a value of no less than 1 as you can see. with a bit of work from the pythagorean theorem i got the other 2 numbers. now on a graph we would express ordered pairs in terms of x and why, but on a unit circle it's express differently. its expressed in terms of sin and cos. x is cos, y is sin.

thats all for today, Jefferson SIGNING OFF!

oh yes

vgamecom!!you're scribe, good luck!and have fun!

:)=3