Circular measure...

[Rutzaba]

okay! here goes nothing...

 

[Rutzaba]

Relation between radian and degrees…


Now im sure you guys know how to turn ur calculators from degree to radians and vice versa…
If not then…
http://www.dummies.com/how-to/content/convert-degrees-to-radians-with-the-ti84-plus-calc.html

In calculations however this is the formula devised to convert degre into rads…
xº (π ) /180º = y radians.

Example
90º (π)/ 180º= π/2 radians

360º (π)/180º= 2 π radians
And if radians need to be converted into degree then
Makingx the subject of formula…

Y radians (180)/ (π)= xº
Example
(π/4)rads (180º) / π =xº
π cancelled by π
(180º/4)= xº
X=45º

 

[Rutzaba]

Area of a sector…
This is sector…
http://upload.wikimedia.org/wikipedia/commons/c/ce/Angle_measure.svg
Formula…
A=0.5 (r²) (Õ)
Where A is the area of the sector,
R the radius,
And theta the angle between 2 radii…


Example

Q.1. A sector has radius 10 cm and Õ= 0.2 radians. Find the area of this sector.
Ans.

Formula…
A=0.5 (r²) (Õ)
A= 0.5 (10²) (0.2)
A= 10 cm²


Q.2. A sector has area 25 cm² and theta = 0.5 radians. What is the radius of this circle?

Ans.

Formula…

A=0.5 (r²)(Õ)
25= 0.5 (r²)(0.5)
r²=100

r=10cm.

2)Arc length

http://upload.wikimedia.org/wikipedia/commons/c/ce/Angle_measure.svg
In the diagram the curved line S is called an arc, its length the arc length

The formula to calculate this is

S=rÕ
This symbol may look like theta Ac=18.0 cm
Where S is the arc length,
R is the radius,
And theta is the angle between the two radii…

Example

Q.1. You have a sector with radius 6 cm and theta =0.3 rads. Find the arc length of this sector?
Ans.
Formula…
S=rÕ
S=(6)(0.3)
S=1.8cm


Q.2. Arc length of a sector is 5 cm. The radius of this circle is 6 cm. Find theta?

Ans
Formula…
S=rÕ
5=6 (Õ)
Õ= 0.83 rads.

Perimeter of the sector…

As you are familiar with ur frend the sector over here…

http://upload.wikimedia.org/wikipedia/commons/c/ce/Angle_measure.svg
You can see the perimeter consists of 2r + S
That is the outline can be found using two lines (r) and 1 arc length (s)
That is

P= 2r +rÕ
Example
Q.1 Find perimeter of sector radius 9 and theta 0.2 rads.
Ans.
2r +rÕ
2(9)= 9(0.2)
18+1.8
19.8 cm.

 

[Rutzaba]

Did I mention?
http://upload.wikimedia.org/wikiped...Circle_slices.svg/220px-Circle_slices.svg.png

The purple thingy is called a segment…
The line at the base of the segment is called a chord…
Any line cutting the circle right from the middle aill be its diameter…
Any line cutting the circle from other than the middle is called a chord…
Length of chord…


http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the length of chord?
Ans
By using cosine rule
http://s3.amazonaws.com/rapgenius/1364467873_cosine_rule.jpg
(Ac)²= a²+b² -2bc cos Õ
(Ac)²= (10.4²)+(10.4²)–2(10.4)(10.4)cos (2π/3)
(Ac)²=216.32–(–108.16)
(Ac)²= 324.48
Area of a segment…


There is no specific formula for this ul just have to pay with the geometry of a circle….
Now consider my words when I say… When I substract the areaof a triangle from the area of a sector I get the area of a segment…
That is

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Example

http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the area of segment ABC?

Ans.

I substract the areaof a triangle from the area of a sector I get the area of a segment…

(120/180)π= 2π/3

Area of segment=

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Area of sector=

0.5 (r²) (Õ)

0.5(10.4 ²)(2π/3) cm²

36.05π

Area of triangle=

0.5 absinc an alternate formula as its short.

0.5 (10.4)(10.4) sin (2π/3)

46.83 cm²

36.05π – 46.83= 66.42 cm²



Perimeter of a segment…


This would consist of an arc length + the length of chord.

Example
http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631
Q.1. Find the perimeter iof the segment.
Ansd. Length Ac + S
Ac as above= 14.7cm
S=rÕ

S10.4*2π/3

S=21.8

14.7 +21.8= 36.5 cm.
Additional note…

*Area of sector/ area of the entire circle =

angle of the sector/ angle of the entire circle.

http://www.1728.org/circpart.htm

 

[Thought blocker]

t y

 

[Rutzaba]

t y

welkx
srry fom the poor editing

 

[Thought blocker]

welkx
srry fom the poor editing

np

 

[kitkat <3 :P]

Did I mention?
http://upload.wikimedia.org/wikiped...Circle_slices.svg/220px-Circle_slices.svg.png

The purple thingy is called a segment…
The line at the base of the segment is called a chord…
Any line cutting the circle right from the middle aill be its diameter…
Any line cutting the circle from other than the middle is called a chord…
Length of chord…


http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the length of chord?
Ans
By using cosine rule
http://s3.amazonaws.com/rapgenius/1364467873_cosine_rule.jpg
(Ac)²= a²+b² -2bc cos Õ
(Ac)²= (10.4²)+(10.4²)–2(10.4)(10.4)cos (2π/3)
(Ac)²=216.32–(–108.16)
(Ac)²= 324.48
Area of a segment…


There is no specific formula for this ul just have to pay with the geometry of a circle….
Now consider my words when I say… When I substract the areaof a triangle from the area of a sector I get the area of a segment…
That is

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Example

http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the area of segment ABC?

Ans.

I substract the areaof a triangle from the area of a sector I get the area of a segment…

(120/180)π= 2π/3

Area of segment=

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Area of sector=

0.5 (r²) (Õ)

0.5(10.4 ²)(2π/3) cm²

36.05π

Area of triangle=

0.5 absinc an alternate formula as its short.

0.5 (10.4)(10.4) sin (2π/3)

46.83 cm²

36.05π – 46.83= 66.42 cm²



Perimeter of a segment…


This would consist of an arc length + the length of chord.

Example
http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631
Q.1. Find the perimeter iof the segment.
Ansd. Length Ac + S
Ac as above= 14.7cm
S=rÕ

S10.4*2π/3

S=21.8

14.7 +21.8= 36.5 cm.
Additional note…

*Area of sector/ area of the entire circle =

angle of the sector/ angle of the entire circle.

http://www.1728.org/circpart.htm

THANK YOUU ^_^

 

[A star]

nice (Y) though I had addmaths so this was never a problem for me always thought it was a mark gainer . ddmaths questions were way tougher -____- (cie logic :/)

 

[Rutzaba]

nice (Y) though I had addmaths so this was never a problem for me always thought it was a mark gainer . ddmaths questions were way tougher -____- (cie logic :/)

had adddmaths here too. p1 and p3 become so easy naturally
i think addmaths was tougher than the p1 and p3 combined

 

[A star]

had adddmaths here too. p1 and p3 become so easy naturally
i think addmaths was tougher than the p1 and p3 combined

nope P3 is much hader but yeah it comes naturally am actually enjoying p3 the key here is though : how to kill the idiot who invented complex nos -______-

 

[Rutzaba]

nope P3 is much hader but yeah it comes naturally am actually enjoying p3 the key here is though : how to kill the idiot who invented complex nos -______-

I KNOWWWWWWWWWWWWWWWWWWWWWW
i enjoyed p3 too.
but i had command over every topic in p3
not in addmaths
relative velocity was tough...

 

[Rutzaba]

nope P3 is much hader but yeah it comes naturally am actually enjoying p3 the key here is though : how to kill the idiot who invented complex nos -______-

our maths sir said i dont have tym.
we pleaded.
he said i have sunday
we said ok
he said 8 am
we said ok
he said three hours we said ok.
when we came out of that class we knew complex numbers...

 

[Rutzaba]

nope P3 is much hader but yeah it comes naturally am actually enjoying p3 the key here is though : how to kill the idiot who invented complex nos -______-

you cant blv tbut we have a lot of darned ill logical theory to study now :'(
pages and pages...
imagine having to rote learn
all the wordings
http://en.wikipedia.org/wiki/Vector_space

 

[A star]

you cant blv tbut we have a lot of darned ill logical theory to study now :'(
pages and pages...
imagine having to rote learn
all the wordings
http://en.wikipedia.org/wiki/Vector_space

I plan to do chemical engineering so maths is their but in fewer ammount

our maths sir said i dont have tym.
we pleaded.
he said i have sunday
we said ok
he said 8 am
we said ok
he said three hours we said ok.
when we came out of that class we knew complex numbers...

Its not the concepts i find hard its the application of those concepts if you solve 10 years you solve atleast 16 different types of questions -___- I mean who does that :/

 

[***amd***]

Did I mention?
http://upload.wikimedia.org/wikiped...Circle_slices.svg/220px-Circle_slices.svg.png

The purple thingy is called a segment…
The line at the base of the segment is called a chord…
Any line cutting the circle right from the middle aill be its diameter…
Any line cutting the circle from other than the middle is called a chord…
Length of chord…


http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the length of chord?
Ans
By using cosine rule
http://s3.amazonaws.com/rapgenius/1364467873_cosine_rule.jpg
(Ac)²= a²+b² -2bc cos Õ
(Ac)²= (10.4²)+(10.4²)–2(10.4)(10.4)cos (2π/3)
(Ac)²=216.32–(–108.16)
(Ac)²= 324.48
Area of a segment…


There is no specific formula for this ul just have to pay with the geometry of a circle….
Now consider my words when I say… When I substract the areaof a triangle from the area of a sector I get the area of a segment…
That is

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Example

http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631

Q.1. Find the area of segment ABC?

Ans.

I substract the areaof a triangle from the area of a sector I get the area of a segment…

(120/180)π= 2π/3

Area of segment=

0.5 (r²) (Õ)–(0.5*base*h )= area of segment.

Area of sector=

0.5 (r²) (Õ)

0.5(10.4 ²)(2π/3) cm²

36.05π

Area of triangle=

0.5 absinc an alternate formula as its short.

0.5 (10.4)(10.4) sin (2π/3)

46.83 cm²

36.05π – 46.83= 66.42 cm²



Perimeter of a segment…


This would consist of an arc length + the length of chord.

Example
http://www.thestudentroom.co.uk/attachment.php?attachmentid=103654&d=1306864631
Q.1. Find the perimeter iof the segment.
Ansd. Length Ac + S
Ac as above= 14.7cm
S=rÕ

S10.4*2π/3

S=21.8

14.7 +21.8= 36.5 cm.
Additional note…

*Area of sector/ area of the entire circle =

angle of the sector/ angle of the entire circle.

http://www.1728.org/circpart.htm

you guys need to learn this? its the easiest of all topics (in Add maths) 0.0

 

[Rutzaba]

you guys need to learn this? its the easiest of all topics (in Add maths) 0.0

lloll

 

[***amd***]

lloll

lol?

 

[Rutzaba]

lol?

yup

 

[***amd***]

yup

why?