Law of sines. Say I have triangle ABC where A=25degrees a=2 and B= 45degrees
C=110 degrees Find the length of side c. to find c use this:
sin(25)/2=sin(110)/c solve for c and you get 2sin(110)/sin(25)=c c=4.447

Pythagorean's theorem. lol ;) A^2+B^2=C^2 (Only works for right triangles)
B=4 C=5 Find A 25-16=9 A=3

Relfection 26

We are finalllllly off for mardi gras :) I really needed a break from school and i'm sure everyone else did too. Anyways I'll review some stuff from chapter 13 because it was the last chapter and I remember stuff the most from that one since it was the most recent. The stuff I didn't talk about in last weeks blogs were series with limits. For limits you have certain rules to follow. *If the degree of the top equals the degree of the bottom the answer would be the coefficient. *If the degree of the top is greater than the degree of the bottom the answser would be infinity. *If the degree of bottom is bigger than top the answer would be 0. *If it's neither then you have to plug the problem into (1/n) or raise it.


Exapmles:

Find the given limit. lim 3n^2 + 5n/8n^2
*Look at your rules and see which one applies.
*You would use the first rule because the degree of the top equals the degree of the bottom.
*So you get 3/8 as your answer

Find the given limit. lim tan(1/n)
*For this problem you would realize it doesn't relate to any of the rules so you would have to follow the formulas for plugging the problem in.
(First you plug in 100, then 1000, then 10000)
*So you get tan(1/100) = .010
*Then you get tan(1/1000) = .001
*Then you get tan(1/10000) = .0001
*Based on the answers you got, it looks that the numbers are getting closer to zero so your answer is zero.

Sorry if anything is a little confusing I don't have my notes and i'm trying to remember everything off the top of my head, haha.

So Im gonna post a reflection on the book we reading called flatland. So flatland is a world that is totally different from ours. In this world everything is a shape. The only thing is that you dont know what shape is what because everyone is sideways so you cannot tell what shape some one is. Imagine looking down at a penny on a table. It appears as a circle, right? Well now lower your head and look parallel to the surface of the table. Now the penny appears as a line, correct? That's what it is like in flatland, they see everything in the type of view you see when you look parallel to the table top. Pretty much how many sides you have is like what race you are. Thats how I look at it atleast. The narrarator is a square. Oh by the way if you are a triangle your kids stay a triangle but if you any other shape then your kids gain a side When you get enough sides to become a "many sided polygon," you are part of the social elite, and if you gain as many sides as to become circular. Thats pretty much as far as i got so far. The next blog will be much more interesting tho:)

Reflection

Flatland is a book about a two-dimensional world. "people" are actually shapes who are distinguished by their shape. Class is determined by the number of sides that you have. Although when it comes to triangles an equalateral is of higher class than an iscoceles. In flatland, houses are pentagonal. Triangle and Square houses are not permited because of their sharp, dangerous edges. The houses have two doors, one for men and one for women. Flatland also has the same poles as us being North, South, East, and West. They distinguish direction from the rain, which always falls from North to South. I think they also distinguish it from some type of attraction that the woman have towards the South pole. But i don't really get that part, can someone please clear that up for me?

reflection

csc x - sin x

1/sin x - sin x/1
multiply sin x/1 by sin x/sin x
1/sin x - sin^2 x/sin x
1 - sin^2 x/sin x
cos^2 x/sin x
= cot x cos x

cot x + tan x
cos x/sin x + sin x/cos x
multiply cos x/sin x by cos x/cos x
multiply sin x/cos x by sin x/sin x
cos^2 x/cos x sin x + sin^2 x/cos x sin x
cos^2 x + sin^2 x/cos x sin x
1/cos x sin x
1/cos x times 1/sin x
= csc x sec x

sin x cot x
sin x/1 times cos x/sin x
sin x cancels out
= cos x

i didnt know if we could do our blogs on something we've learned or if it had to be on flatlan

REFLECTION #26

okay so this is the latest i've ever done a reflection ha. um i believe we learned sequences and series recently so i'll go over those before anyone forgets how to do them. and by the way i dont have any of my notes with me so me remembering this off the top of my head is quite an accomplishment thank you very much. so here it goes. (and yes i made up all these examples so if they don't work thats why (; )

Starting from the beginnning of Chapter 13..

Ex 1.) Find the 32nd term in the sequence: 1,4,7,10...
*Okay the first thing you have to do is figure out whether this sequence is arithmetic or geometric.
*It's arithmetic. you know this because you are adding 3 each time.
*for this problem you are going to be using the arithmetic formula: tn=t1+(n-1)d
*And since you are looking for the term number you are looking for "n" in the formula. So you plug in 32 wherever "n" is in the formula.
*So you get t32=1+(32-1)(3)
*that simplifies to =1+(31)(3)
*So t32=94

Ex. 2.) Find a formula for the sequence: 2,4,8,16,32,...
*First figure out whether it's arithmetic or geometric.
*It's geometric and your ratio is 2
*since it's geometric you're going to use the formula: tn=t1(r)^n-1
*And since you're just finding a formula, all you have to do is plug in the numbers that you are given
*And you get>> tn=2(2)^n-1 and that's your formula

Ex. 3) How many multiples of 3 are there between 10 and 250?
*Okay with problems like these, the first thing you want to do is find the smallest multiple of 3 and the largest multiple of 3 that are between those numbers.
*So you get that 12 is the first multiple of 3 between those numbers and 249 is the last multiple of 3.
*And you form a sequence out of it like this: 12 being the first term, 15 being the second because that's the next multiple, then 21, ...and so one until the last number which is 249
*so your sequence would look like this: 12,15,21,...249
*now you have to see if it's arithmetic or geometric
*its arithmetic because you add 3 each time
*Then you just plug the numbers you know into the arithmetic formula: tn=t1+(n-1)d
*So you get 249=12+(n-1)(3)
*249=12+3n-3
249=9+3n
240=3n
*So the answer is 80

Well I think I've done enough reviewing for one week. Happy Valentine's Day everyone (:

Valentine's Day Reflection

Well this week i'm goin to reflect on the book we are reading which is incredibly amazing (cough cough) Okay so flatland is a world where everything is different from our world, which the main character calls "spaceland." Imagine looking down at a penny on a table. It appears as a circle, right? Well now lower your head and look parallel to the surface of the table. Now the penny appears as a line, correct? That's what it is like in flatland, they see everything in the type of view you see when you look parallel to the table top. Now as far as social classes, it is pretty simple, it goes by how many sides you have. Oh yea, did i forget to mention that "people" are shapes in flatland? The narrarator, just for your information, is a square. I know, intense right? All women are straight lines, that part's stupid. Anyway, triangle are the lowest social class. They are workers and soldiers, and their offspring will also be triangles. Squares' offspring, though, gain one side when they born, so a square's kid is a pentagon. So the more sides you have the higher up in the social world you are. When you get enough sides to become a "many sided polygon," you are part of the social elite, and if you gain as many sides as to become circular, you are the highest of the high. People in flatland find their way around by using a natural southward pull. So sort of like we always know where north is because of a compass, they always know where south is because a natural pull (like an internal compass) south. I know, uncredibly interesting right?

**NOTE** If you are not plannin on readin the book, you sir, are an idiot, cuz if you get behind on this confusingness you have no shot.....

1st Mardi Gras Reflection

Flatland is about a square who is a resident of a two-dimensional Flatland, where women are thin straight lines are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
There are four points of the compass North, South, East, and West. There being no sun or heavenly bodies, it is impossible for them to determine the North in the usual way; but they have a method of their own. By the Law of Nature, there is a constant attraction to the South; and, althogh in temperate climates this is a very slight, so that even a Woman in resonable health can journey several forlongs northward without much difficulty.
All in all, that means that the shapes have their own world and can tell whats going on inside their world. When another shape approaches, it looks like a sailor on a ship approaching an island. A flat line that magically appears to look different upon arrival.
So far, this book seems very boring to me, hopefuly that changes as the chapters go on. IF anyone else would like to explain what is going on in this book, i would appreciate it, aha , cause i d not really understand fully what is going on in thee first four chapters. THanks much!!

Reflection #26

Okay, I'm going to review Identities:

csc x = 1/sin x
sec x = 1/cos x
cot x = 1/tan x
sin (-x) = -sin x
cos (-x) = cos x
csc (-x) = -csc x
sec (-x) = sec x
tan (-x) = -tan x
cot (-x) = -cot x
sin^2 x + cos^2 x = 1
1 + tan^2 x = sec^2 x
1 + cot^2 x = csc^2 x
sin x = cos (90 degrees - x)
tan x = cot (90 degrees - x)
sec x = csc (90 degrees - x)
cos x = sin (90 degrees - x)
cot x = tan (90 degrees - x)
csc x = sec (90 degrees - x)
tan x = sin x/cos x
cot x = cos x/sin x

Examples:
csc x - sin x
1/sin x - sin x/1
multiply sin x/1 by sin x/sin x
1/sin x - sin^2 x/sin x
1 - sin^2 x/sin x
cos^2 x/sin x
= cot x cos x

cot x + tan x
cos x/sin x + sin x/cos x
multiply cos x/sin x by cos x/cos x
multiply sin x/cos x by sin x/sin x
cos^2 x/cos x sin x + sin^2 x/cos x sin x
cos^2 x + sin^2 x/cos x sin x
1/cos x sin x
1/cos x times 1/sin x
= csc x sec x

sin x cot x
sin x/1 times cos x/sin x
sin x cancels out
= cos x