Difference between revisions of "Sector"
I like pie (talk | contribs) m (Removed unnecessary stuff) |
I like pie (talk | contribs) m (Changed Asy image slightly) |
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<div style="float:right"><asy>size(150); | <div style="float:right"><asy>size(150); | ||
| − | real angle1=30, angle2= | + | real angle1=30, angle2=120; |
pair O=origin, A=dir(angle2), B=dir(angle1); | pair O=origin, A=dir(angle2), B=dir(angle1); | ||
path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; | path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; | ||
| Line 7: | Line 7: | ||
D(A--O--B); | D(A--O--B); | ||
MP("O",D(O),SSW); | MP("O",D(O),SSW); | ||
| − | MP("A",D(A), | + | MP("A",D(A),NW); |
MP("B",D(B),NE); | MP("B",D(B),NE); | ||
| − | MP("\theta",(0. | + | MP("\theta",(0.05,0.075),N);</asy></div> |
A '''sector''' of a [[circle]] <math>O</math> is a region bounded by two [[radius|radii]] of the circle, <math>OA</math> and <math>OB</math>, and the [[arc]] <math>AB</math>. | A '''sector''' of a [[circle]] <math>O</math> is a region bounded by two [[radius|radii]] of the circle, <math>OA</math> and <math>OB</math>, and the [[arc]] <math>AB</math>. | ||
Revision as of 20:54, 24 April 2008
![[asy]size(150); real angle1=30, angle2=120; pair O=origin, A=dir(angle2), B=dir(angle1); path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; fill(sector,gray(0.9)); D(unitcircle); D(A--O--B); MP("O",D(O),SSW); MP("A",D(A),NW); MP("B",D(B),NE); MP("\theta",(0.05,0.075),N);[/asy]](http://latex.artofproblemsolving.com/7/c/9/7c9a7756f90fe421d7f60125f66669fa9200d25d.png)
A sector of a circle 
is a region bounded by two radii of the circle, 
and 
, and the arc 
.
Area
The area of a sector is found by multiplying the area of circle by 
, where 
is the central angle in radians.
Therefore, the area of a sector is 
, where 
is the radius and is the central angle in radians.
Alternatively, if is in degrees, the area is 
.
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