Sector of a circle

Formulas:
1. s=(r)(theta)
(s= arch length) (r= radius) (theta= central angle)

2. k= (1/2)(r^2)(s)
(k= area of the sector)

3. k= (1/2)(r)(s)

Next here are your steps:
1. find out what is given.. for example s=? r=? k=? and theta=?
You must find at least two of these in order to figure out this problem.

2. you are going to want to make sure that theta is in radians.
if theta is in degrees then you need to multiply that by (pie/180) to convert degrees into radians.

3. next, you are going to need to choose one of the formulas to plug into.
you want to choose the formula that works best with the problem.
for example if you have s= 4 cm and k= 36 cm you are not going to want to choose formula #1.
you would want to choose formula #3.

4. then, after you find one of the missing variables you will have one more variable still to find.
so, you are going to plug into another equation that fits the found variables and plug into the appropriate equation.

Here is an EXAMPLE:
A sector of a circle has an arc length of 4 cm and an area of 52 cm^2. Find its radius and the measure of its central angle.

So now follow the steps..
What are the given variables?
s= 4cm k=52cm^2 r=? theta=?

Now you must use the appropriate formula
formula #3 will work the best. [k=(1/2)(r)(s)]
52cm^2=(1/2)(r)(4)
52cm^2=2r
r= 26cm

Now that you found the answer for the variable r you can plug into another formula to find theta.
the best fit formula to find theta is formula #1 [s=(r)(theta)]
4cm= (26cm)(theta)
theta=(1/6 radians)

This is how you find the sector of the circle, and have a great new year.

Lovin' some math over my holidays.

So, as we all know i do not remember anything that is going on with school and i am pretty sure i am not the only one. I see everyone posting blogs about what we learned in certain chapters, but i will be fair and not copy what they are putting. I will also confess that i do not have my binder therefore i cant exactly say anything we had learned. Actually, this may not even count as a blog because there is nothing to do with math in this but atleast i still came to this website. Well, like some other people i can openly say that I would not be surprised if i failed the midterm. I guess we will have to see when the grades come back, BUT my luck..my family decides i will leave for a 8 day vacation the day of the hardest exam ever! I do know that school comes first, but i honestly packed instead.. I did read over everything for the exam but it just doesn't click to me. Don't get me wrong i do try, i just will never understand. Well i'm gonna stop exposing myself now and check out those prompts i didn't do yet..

Happy New Year! :)

13-6

13-6 is all about sigma. A sigma is a series written in condensed form. The sigma is representing with F because I’m too lazy to make it.

The Sigma contains three parts. The summand is the limits of summation, and the index. The number to the right of the Sigma is the summand. The number on top of the Sigma is the limits of summation. The number on the bottom of the Sigma is the index. You can either be asked to expand the Sigma or evaluate the sigma. To expand you only plug the numbers was they need to go. To evaluate you solve the whole thing.


The greek letter sigma is often used in mathematics to express a series or its sum in abbreviated form.

6
F4k
K = 2

Find the Summand? 4k
What is the index? k
What are the limits of summation? 5 and 2

Evaluate the Sigma

4(2) + 4(3) + 4(4) + 4(5) + 4(6)
8 + 12 + 16+ 20 + 24 = 80

Basically 13-6 is easy but it can mess you over if you don't know all the information about stigma if you do you will easily breeze threw this section.

11-2

In chapter 11 section 2 it is dealing wit complex numbers.

Rectangular= -2=x+yi

Polar= -2=rcostheta+rsinthetai-> from 11-1
If u want to abbreviate to 2=rcis

To multiply complex numbers

Rectangular – foil

Polar – multiply r; add thetas


Express
2cis45degrees to rectangular

x=rcostheta=2cos45degrees=2(square root of 2/2)=square root of 2
y=rsintheta=2sin45degrees=2(square root of 2/2)=square root of 2

z=square root of 2+square root of 2 i


Express 2
Z=1-square root of 3 in polar
Square root of 1^2 +square root of 3^2=1+3= square root of 4 = +/-2

Tan –square root of 3/1=theta=tan^-1square root of 3

60 where it – second Q and 3rd .

Q2= 120degrees Q3= 300 degrees.

Z=2cis300degrees
Z=2cos300degrees+2sin300degreesi
Z=-2cis120degrees
Z=-2cos 120degrees+-2sin 120degreesi
All you answer above

Z1*Z2

Z1 2cis 30 z2 3 cis 20

= 6cis 50degrees

Basically section11-2 is weird long and aggravating. If you know what you are doing and know all your formulas it will be easy for you

9-3

In chapter 9 section 3 it is dealing with the law of sines. The law of sines has 2 steps to follow: used with non-right triangles, only use when you have an angle and opp leg value you know.

The formula for law of sine is sin(angle)/opp leg=sin(angle 2)/ opp leg 2
*cross multiply to solve

Example is in triangle rst if so find all possible measure of
Sin 126^o/12* sin t/7=12sint=7sin126= sin t= 7 sin 126degrees/12

You get 28.159degrees which is your answer.

Example 2:
Solve for x if one angle is 60 degrees another 25 degrees and a side is 8.
Sin 60 degrees/8=sin 25degrees/x = xsin60degrees=8sin25degrees you divide sin 60 degrees you get 3.904 as your answer.

Basically law of sine can be tricky at times but if you on a role and know everything you will make law of sine your pet and own at it.

8-1

In Section 8-1 to solve for theta you get the trig function by itself and then take an inverse.
An inverse has 2 answers with some exceptions; find where the angle is based on trig function and if number +ve or –ve.

Steps: take the inverse of +ve number to find the Q1 angle.

To get to
Q2 make –ve degree add 180
Q3 add 180 degrees
Q4 make +ve add 360 degrees

Example:

3 cosine(theta)= 1

1. Subtract 3 from one, which will equal -1/3
2. Then do the cosine inverse(1/3)=
70.529
3. We are looking for the positive cosine, which is x.
4. 70.529 degrees is in the first quadrant, so it is positive.
5. Since it is in the first and fourth quadrant, for fourth quadrant, we will do 360-70.529, and it will equate to 289.471 degrees

Answers: 70.529(degrees), 289.471(degrees).

If u know everything in 8-1 and the formulas u will do fine and it will be a breeze.

The confusing Chapter 13

Happy New Years everyone! Chapter 13 is still pretty hard for me being I never really understood the concept. In this particular section I was able to clearly understand what it was telling you to do, but when I had to plug into the calculator I struggled to tell whether it was reaching 1 or 0. Besides knowing where the numbers were aiming to, you needed to remember all of the guidelines which sometimes where hard to not mix up.

Guidlines for this Chapter:

For Fractions:
1. If the top degree = bottom degree the answer is a coefficient.
2. If the top degree > bottom degree the answer is +/- infinity.
3. If the top degree < bottom degree the answer is 0. If the rules above do not apply to the given, then you simply use the table function in your calculator.

For example:

1. Lim/n->infinity n^7 +6/ 9n^2 – 7n

The degrees are 7 and 5.

The top one (7) is larger than the bottom one (2).

When you look at your rules, they state that the answer will be +/- infinity.

Happy New Years once again and see yall Monday (: