Unit 3

Unit three. Trig Identities. What can I say? It's pretty easy. You just have to know what to do. That's all.

UNIT 3

Well what can i say? it was pretty good. I got some of the stuff. Some are very confusing. It take a lot of practice to get the hang of it. That's all. Good luck everyone on the test!!! =)

Unit 3

I really enjoyed this unit. This is the unit that i REALLY understand. I hope i pass this test. Hehe. That's all!

HOW I FEEL ABOUT UNIT 3

Ok, well I'm going to say that I actually felt a bit confident about this unit. I think I'm just hallucinating though, because last unit I thought I was going to fail - yet I passed. I think it's just the homework that's been killing my mark. I have been doing the exercises but I guess I should start focussing more on assignments worth marks. AHH I'm scared for the test today. Good luck everyone.

...

I think this unit is okay. But I am having some hard time working with fractions.
GOOD LUCK ON THE TEST TOMORROW!

TRIG IDENTITIES

holy moly, the test is tomorrow...gotta study to get a good grade. hopefully this test i do good on because i understand it more than the other. well that's what i said on the last test but i did ehh. but whatev. uggh this unit was pretty easy in the beginning but todays pre test was reeeeaaall hard. but afterwards when i got help from mrs.ingram i was like "WHOA! this is super easy." i just needed to know the triangles and yeea i just over think this and thats why i do bad. but for sure ill do my best for this test. because this is the last assignment for term one and then we get our report cards. but lets not think about that. i really like this unit your just looking for cos and sin and then you plug it in. i just understood all this just today. thats good. anyways im blabbing on so i think i should stop...okay well good luck to every single one of you for tomorrow's test. we gotta do good! k let's do this!! kk bye.

DIFFERENCE AND ADDITION IDENTITIES

MORNING NOTES


This is called a co function property for circular functions.

Which can be written like this:

sin (pi/2 - x) = cosx or cos (pi/2 - x) = sinx

cot (pi/2 - x) = tanx or tan (pi/2 - x) = cotx

csc (pi/2 - x) = secx or sec (pi/2 - x) = cscx



ex) Can you find the value for cos15? (W/out your calculator)

-you should know 0, 30, 45, 60, 90, 180, 270.
Using these values we’ll get to cos15

Which values if you subtract or add you’ll get 15?
Cos(45-30)



coordinates for d1
p1 - coordinates of p(α) (cosα , sinα)
p2 - coordinates of p(β) (cosβ , sinβ)

coordinates for d2
p3 - coordinates of p(α-β) (cos(α-β) , sin(α-β)
p4 - coordinates of p(P0) (1,0)

we will be using the distance formula
d= (square root)(x2-x1)^2 + (y2-y1)^2

d=(square root)(cosβ- cosα)^2 + (sinβ-sinα)^2 = (square root)(cos(α-β)-1)^2 + (sin(α-β)-0)^2


(root)(cos^2β-2cosβcosα+cos^2α + sin^2β-2sinβsinα+sin^2α
(root)(cos^2β+sin^2β+cos^2α+sin^2α-2cosβcosα-2sinβsinα
(root)(1)(1) - 2cosβcosα-2sinβsinα
((root)2-2cosβcosα-2sinβsinα)^2 <----we square it to get rid of the root sign

=

(root)cos^2(α-β)-2cos(α-β)+1 + sin^2(α-β)
(root)cos^2(α-β)+sin^2(α-β)-2cos(α-β)+1
(root)(1) + (1) - 2cos(α-β)
((root)2-2cos(α-β))^2 <----we square it to get rid of the root sign


we do this because we're trying to get to a point where it's cos(α-β)

2-2cosβcosα-2sinβsinα = 2-2cos(α-β) <--2's cancel
-2cosβcosα-2sinβsinα/-2 = -2cos(α-β)/-2 <--divide both sides by -2 to get rid of the denominator

and you get

cosβcosα+sinβsinα = cos(α-β) <--this is called difference identity


as you can remember from beofre we were trying to look for cos15.
we can also do this cos(45-30) <--45 is the α and 30 is β

cos(45-30) = cos45cos30 + sin45sin30
=(root2/2)(root3/2) + (root2/2)(1/2)
=(root6/4) + (root2/4)
=root6 + root2/4

now addition....

cos(105) **it doesnt matter whether you multiply (α)(β) or (β)(α) <--it's still the same thing

so...
cos(105)
what can you add to get 105 from the numbers : 0, 30, 45, 60, 90, 180, 270 ?
60 and 45 . .riiight?

cos(60+45)
cos(α+β) = cos(α-(-β))
-------- =cosαcos(-β) + sinαsin(-β)
-------- =cosαcosβ - sinαsinβ


we can say that cos(-β)=cosβ

so the addition identity is written like this...
cos(α+β) = cosαcosβ-sinαsinβ

AFTERNOON NOTES

use identities to find the exact value for 7pi/12 and cos 7pi/12

we know : 0 , pi/6 , pi/3 , pi/4 , pi/2 , pi , 3pi/2 , 2pi

pi/3 = 4/12
pi/4 = 3pi/12 . . . we get 7pi/12



sin(pi/3 + pi/4) = sin(pi/3)cos(pi/4) + cos(pi/3)sin(pi/4)
---------------- =(root3/2)(root2/2) + (1/2)(root2/2)
---------------- =(root6/4) + (root2/4)
---------------- =(root6 + root2)/4

cos(α+β)= cosαcosβ - sinαsinβ
cos(pi/3 + pi/4)= cos(pi/3)cos(pi/4) - sin(pi/3)sin(pi/4)
----------------= (1/2)(root2/2) - (root3/2)(root2/2)
----------------= (root2/4) - (root6/4)
----------------= (root2 - root6)/4

yess! finally im done. hopefully you all understand. this took pretty long but i had fun with it. so the next scribe i choose well not really is nikka-elle... good luck nicky :)

Unit Two. This unit wasn't too bad. At first, it was pretty easy. I pretty much understood everything we've learned. However, I still have to practice a bit more on writing the Cosine and Sine equations from looking at graphs. They're not that bad, I just need more practice. Also, I hate those word problems. They make it sound so confusing, but when you actually do it WITH THE TEACHER, it seems easy. When you do it yourself, it's sort of... hard? Yeah. But that's okay, that's what the homework is for, right? Speaking of which, I should study. So... I'm done.

UNIT TWOOO

Ahh...I just got home from work. Its getting prety late. ANYYWAYYSS....uhh. Yeah, Unit two. It was pretty hard. Pretty confusing. I get confuse with that sinusodal or is it sinusodial? hmm...but you know what I mean. Transformation is pretty easy. Wow, precal is getting harder. I'd rewrite my notes over again to understand it. But like I said its getting pretty late. Well I can't think of anything else to write so like everyone says...

GOODLUCK ON THE TEST TOMORROW EVERYONE !!! =)

haha and oh i'm pretty proud of myself...im not late anymore. well not as much. hehe. I don't even know why I put that. -_-"

well, goodnight.

Unit 2 blog.

This unit is alright I guess. It's true that if you don't pay attention you will have a hard time doing the questions. I'm still not used to not having notes for the whole period. I like it when we take lots of notes and do the questions afterwards. I don't know... I'm just not used to how it is yet.... I'm so scared I might fail this class. I could've tried this unit but MAAAN! I'm losing my focus. pfft. I will try now and I will start studying...

I think its great idea to have weekly goals. I think I will set one up for this class starting this week.... *sigh*

ANYWAYS...

I gotta go study my notes now...
Good luck everyone.

HOW IT'S GOING SO FAR?

for me... hmm... i think that this unit is easier than the other one...i dont know why. but i understand it much better. just hopefully i get a good mark on this test. but gotta study real hard tonight... yeeah. i think it's going good so far hopefully i dont screw up... XD

HOW I FEEL ABOUT UNIT 2

I actually don't really know how I feel. I'm gonna be honest and say that I think I probably get 30% of the material. I want to do really well on the test tomorrow though. Compared to the last unit, I think it's a lot easier so hopefully my mark will go up -HOPEFULLY.

Sinusoidals

Sinusoidals

-a function which can be written in the form of f(x)= asin(bx+c)+d or
f(x)= acos(bx+c)+d where a,b,c & d are real nos.

There are formulas to get the value of the ff so u can easily graph the equation:
(let's just pretend that # is a pie sign and [ ] is an absolute value except for the Range)

Period: 2#/[b] or 2pie over absolute value of b

Amplitude: [a] or abs value of a

Phase Shift: -c/b

Maximum: d + [a]

Minimum: d - [a]

Range: (d + [a], d - [a])

let's have a 1st ex:
Sketch: y=sin4x

1st thing to do is: label a,b,c,d
a = 1(coefficient of sin)
b = 4(coefficient of x)
c=0 }
d=0 } there's no c & d at this given equation

...to get the period, use the formula that i gave u..

Period= 2#/[b] = 2#/[4]= #/2

as well as the other ones..

Amplitude = [a] = [1] = 1

Phase Shift = -c/b = -(0)/4 = 0

Max = d + [a] =0 + [1] = 1

Min = d - [a] =0 - [1] = -1

so the Range will be: [-1,1]

here is another ex:

Sketch: y=cos(O - #/2)

a=1

b=1
c=-#/2

d=0

Period: 2#/[b] = 2#/[1]= 2#

Amplitude: [a] = [1] = 1

Phase Shift: -c/b = -(-#)/2 = #/2

Max: d + [a] = 0 + [1] = 1

Min: d - [a] = 0 - [1] = -1

Range: [-1, 1]

Sorry about the blog im really not good in making one. I was really having a hard time doing this and to explain it as well..so yah guys just try to understand it.