Almost forgot to do a blog again! Better late than never,right? Okay, this week I'll be reviewing permutations and combinations. Permutations and combinations are formulas used to find different ways something can be ordered. The difference between a permutation and combination is that you use a permutation when the order is important and you use a combination when the order is NOT important. Some things to know: The formula for a permutation is n!/(n-r)! The formula for a combination is n!/(n-r)r! Your n will ALWAYS be larger than you r. Let's do some examples to help you better understand. Example 1: 5P3 5P3=5!/(5-3)! =5!/2! =5*4*3*2*1/2*1 = 60 Example 2: 5C3 5C3=5!/(5-3)3! =5!/2!3! =5*4*3*2*1/2*1*3*2*1 =20/2 =10 And that's all there is to it.

almost forgot to do another blog!!

well im BUKU tired and i cant believe i just took out my laptop to do this.
i saw somebody write the trig chart i think so thats what im doing. i can barely type im so tired

sin 0= 0

sin pi/6=1/2

sin pi/4= square root of 2/2

sin pi/3= square root of 3/2

sin pi/2= 1 



cos 0= 1

cos pi/6= square root of 3/2

cos pi/4= square root of 2/2

cos pi/3= 1/2

cos pi/2= 0




csc 0= undefined

csc pi/6= 2

csc pi/4= square root of 2

csc pi/3= 2 square root of 3/3

csc pi/2= 1




sec 0= 1

sec pi/6= 2 square root of 3/3

sec pi/4= square root of 2

sec pi/3= 2

sec pi/2= undefined




tan 0= 0

tan pi/6= square root of 3/3

tan pi/4= 1

tan pi/3= square root of 3

tan pi/2= undefined




cot 0= undefined

cot pi/6= square root of 3

cot pi/4= 1

cot pi/3= square root of 3/3

cot pi/2= 0

who doesnt love the trig chart? idk but i better get credit because even tho it looks like i did nothing, this was the hardest blog yet considering how tired i am!

goodnight bloggers

you'd think after all this time i'd remember to blog before 10:00 sunday night...you'd be wrong.

This week I am going to review the oh so exciting concept that is multiplying matrices. Pay attention…this is a toughy.

In order to multiply matrices, the dimensions have to be precise. You must have the same number of columns in the first matrix as rows in the second matrix. If you do not have such dimensions, YOU CANNOT MULTIPLY. If you do not have proper dimensions, the answer is not defined. DO NOT CONFUSE THIS WITH UNDEFINED. Undefined means you have divided by zero. NOT DEFINED means no solution.

-Helpful hint, after multiplying, your answer matrix will have the same number of rows as the first matrix and columns of the second matrix.

Example:
[3 4] [2 3 1] [22 33 23]
[6 7] X [4 6 5] = [40 60 41]
[9 1] [22 33 14]

Since the dimensions of the first matrix are 3x2 and the dimensions of the second matrix are 2x3, your answer matrix will be a 3x3.

First, multiply row one by column one. (I’m going to fill answers into the matrix as I go)
3(2)+4(4)=22

First row second column, then first row third column.
3(3)+4(6)=33 3(1)+4(5)=23

Continue the same process with rows two and three.

That is all.

--Sarah

Review of De Moivre's Theorem!

Soo today, we are going to learn all about De Moivre’s theorem! As I said in an earlier blog, chapter 11 consists of a few formulas to be followed. Most of them are really easy. (Especially in this section because there is only one that you must know J) It is pretty simple if you follow the theorem exactly how it is stated. There is one thing that you need to keep in mind throughout this section and that is:

**DO NOT DRAW ARGAND DIAGRAMS**


De Moivre's theorem states the 2=rcisø then z^n=r^n cis(nø)


So now for the emphasis example!


Evaluate (2sin45)^2

z^2=2^2cis2(45)
z^2=4cis90

Since I don't think I hit a 150 words yet, I'll do a problem like this but working backwards.


z=4cis20º (Use De Moivre's theorem to find z^3)

z^3=(4)^3cis(3(20))
z^3=64cis60

So basically if you know and learn De Moivre's theorem, you can work any of these problems.


Hope you learned something!

Carleyyyy :) have a greatttt week!!

11-2

Things you should know:

• z = x + yi
• z = rcostheta + rsintheta i 
• z = rcistheta
• |z |= square root of x^2 + y^2
• To multiply complex numbers:

1. Foil for rectangular problems.
2. Multiply r and add theta for polar problems.

Example: 0 + i

What form is it in? Rectangular form.

Find r and theta.

r = square root of 0^2 + 0^2. 

r = 0 + 0 =0

theta = tan^-1(0)

 Theta = 0

When you put that on the quadrants, you will get 180 and 360.

So once you do that, your answers will be square root of 2 cis 180 degrees and -square root of 2 cis 360 degrees.

Example 2: 10 cis 20 degrees

• What form is it in? Polar form.
• Solve for x and y.
• x = 10cos20= 9.367
• y=10sin20= 3.420
• Final answer: 9.367 + 3.420

-Amber :P

13-1 Review

This week I am going to review with you all the information that we learned in chapter 13, section 1. In chapter 13, section 1, we learned about arithmetic and geometric sequences. In this section, we just learned the basics of geometric and arithmetic sequences. Here are the notes.

Notes:
• An arithmetic sequence is a sequence that is generated by adding the same number each time.
• The formula for an arithmetic sequence is as follows: tn = t1 + (n – 1) d
• A geometric sequence is a sequence that is generated by multiplying the same number each time.
• The formula for a geometric sequence is as follows: tn = t1 * r^(n – 1)
• n = number of terms
• tn = term number
• t1 = term 1
• d = what is added
• r = what is multiplied

Example: Identify the following as an arithmetic or geometric, and find the formula for the nth term: 3, 6, 9, 12, ……
• this is an arithmetic sequence
• tn = 3 + (n-1) 3
• tn = 3 + 3n-3
• tn = 3n




-Braxton-

13-4

today im going to teach you how to do infinite limits. this is a review because i taught this before and we went over it. some key notes to know is that if:
1) (degree)top=(degree)bottom then limit = lead coeff / leading coeff.
2) (degree)top > (degree)bottom then limit = +/- (infinity)
3) (degree)top < (degree)bottom then limit = 0
* if it doesn't follow rules then yoy plug into y= in calculator, 2nd table, plug in 10|100|1000|10000
until you see a pattern*
4) E +ve # = + or - inf
    E -ve # = 0
*if it is geometric & |R| < 1 then limit = 0. if |R| > 1 the limit = (infinity)

EX's:
1) lim/ n (infinity)   n^3 + 2n^2 + 6 / n^2 - 4n^3
so (degree)top = (degree)bottom = -1/4

2) lim/ n (infinity)  n^3 + 2n^2 + 6 / n^2
 so (degree)top > (degree)bottom = +(infinity)

3) lim/ n (infinity)  5n - 5 / n^2
so (degree)top < (degree)bottom = 0

Review of the Trig Chart

So since all we did this week was take tests and review for some more tests. I am going to just review the oh so wonderful and important trig chart.

sin 0= 0

sin pi/6=1/2

sin pi/4= square root of 2/2

sin pi/3= square root of 3/2

sin pi/2= 1 



cos 0= 1

cos pi/6= square root of 3/2

cos pi/4= square root of 2/2

cos pi/3= 1/2

cos pi/2= 0




csc 0= undefined

csc pi/6= 2

csc pi/4= square root of 2

csc pi/3= 2 square root of 3/3

csc pi/2= 1




sec 0= 1

sec pi/6= 2 square root of 3/3

sec pi/4= square root of 2

sec pi/3= 2

sec pi/2= undefined




tan 0= 0

tan pi/6= square root of 3/3

tan pi/4= 1

tan pi/3= square root of 3

tan pi/2= undefined




cot 0= undefined

cot pi/6= square root of 3

cot pi/4= 1

cot pi/3= square root of 3/3

cot pi/2= 0

you also might need to know these few things.

pi/6= 30 degrees, pi/4= 45 degrees, pi/3= 60 degrees, pi/2= 90 degrees, sin=sine, cos=cosine, csc= cosecant, sec=secant, tan=tangent, cot=cotangent.

so that's it. later
Brad

Review of 11-2

So this week I am going to do my blog on a review of section 11-2. This section is on problems with complex numbers. This should be very simple and easy to remember. So I'll get started by giving you a few formulas.

• z=x+yi
• z=rcos theta + rsin theta i
• z=rcis theta
• |z|=square root of x^2 + y^2 

Note: To multiply complex numbers:

• With rectangular problems remember to always foil.
• With polar problems you will multiply r and add theta.

okay, so now I'll do an example for you. I might even do two examples, but it depends.

Example: -1 + i

Since it is in rectangular form, you are going to find r and theta.

r=square root of -1^2 + 1^2. Which equals square root of 2.

theta=tan^-1(-1). Which equals 45.

When you put that on the quadrants, you will get 135 and 315.

So once you do that, your answers will be square root of 2 cis 135 degrees and -square root of 2 cis 315 degrees.

Example 2: 6 cis 100 degrees

• x=6 cos 100= -1.042
• y=6 sin 100= 5.909
• Your answer is going to be -1.042 + 5.909

so, that's it for this week. Hope I helped you remember how to work these problems. byee.

--Halie!

Ch. 13 Review

13-1
This week I'm going to do a review on 13-1 where we learned about arithmetic and geometric sequences. We learned how to identify a sequence as arithmetic or geometric, how to find the nth term in a sequence, and how many terms are in a sequence. We also learned how to find the mean for both types of sequences.
-arithmetic sequence: sequence that is generated by adding the same number each time
  formula: tn = t1 + (n-1)d
-geometric sequence: sequence that is generated by multiplying the same number each time 
  formula: tn = t1 x r^(n-1)
-arithmetic mean: a + b/2
-geometric mean: square root of ab


Example 1: Identify the following as arithmetic or geometric and find the formula for the nth term.
4,8,16,32,...
-geometric
-tn = t1 x r^(n-1)
        4 x 2^(n-1)
        4 x 2^n x 2^-1
        4 x 2^n/2
        = 2 x 2^n


Example 2: Find the indicated term of the arithmetic sequence.
t1 = 3, t4 = 12, t30 = ?
- 3 + d + d + d = 12
  3 + 3d = 12
  3d = 9
   d = 3
-t30 = 3 + (30 - 1) (3)
 = 90

Trig Reviewwww

Today we are going to do some review from the trigonometry section. If you do remember Trig, you are good to go and can probably work my examples right now. But incase you don’t remember everything; all you need to know right now in trig is basically formulas as well as the trig chart. For starters, you must remember:

· Sin=1/csc

· Cos=1/sec

· Csc=1/sin

· Sec=1/cos

· Tan=1/cot

· Cot=1/tan

· Tan=sin/cos

Apart from knowing that, you must also know the Pythagorean Identities. To refresh your memories, these are the Identities you will need to use when doing a lot of trigonometry.

· Sin^2+cos^2=1

· 1+tan^2=sec^2

· 1+cot^2=csc^2

Now that we’ve went over some of the basic things needed to work the examples I am about to show you, we can begin J

Example 1: Simplify:

(Sinx^2+Cosx^2)/ Sinx

1. Look for identities. You have one, so simplify it.

2. You now get 1/Sinx. You can simplify this by referring to the notes above.

3. You get Cscx as your final answer J

I hope this review helped!

CARLEYYYYY