Find the Area in polar coordinates

In summary, the formula for finding the area in polar coordinates is A = 1/2 ∫<sub>θ<sub>1</sub></sub>θ<sub>2</sub> r² dθ, and to convert from polar coordinates to rectangular coordinates, you can use x = rcosθ and y = rsinθ. The area in polar coordinates cannot be negative and is always a positive value. The main difference between polar coordinates and rectangular coordinates is the use of an angle and radius versus x and y coordinates. To find the area of a sector in polar coordinates, you can use the formula A = 1/2 r²θ.
  • #1
MozAngeles
101
0

Homework Statement


I am doing even problems in my book to study and i want to check this answer to see if it is right.
q: Find the area enclosed by one leaf of the three-leaved rose r=sin3(theta)


Homework Equations



A= integral 1/2 r2 d(theta)

The Attempt at a Solution


i used the formula setting the limits from 0 to pi/3 i got my answer to be pi/12 is this right?
 
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  • #2
Yes, your answer is correct:

[tex]
A=\frac{1}{2}\int\limits_{0}^{\frac{\pi}{3}}
[sin(3\theta)]^{2} d\theta = \frac{\pi}{12}
[/tex]
 

FAQ: Find the Area in polar coordinates

What is the formula for finding the area in polar coordinates?

The formula for finding the area in polar coordinates is A = 1/2 ∫θ1θ2 r² dθ, where r is the radius and θ1 and θ2 are the starting and ending angles, respectively.

How do you convert from polar coordinates to rectangular coordinates?

To convert from polar coordinates to rectangular coordinates, you can use the following formulas: x = rcosθ and y = rsinθ, where r is the radius and θ is the angle.

Can the area in polar coordinates be negative?

No, the area in polar coordinates cannot be negative. It is always a positive value since it represents the magnitude of the region enclosed by the curve.

What is the difference between polar coordinates and rectangular coordinates?

The main difference between polar coordinates and rectangular coordinates is that polar coordinates use an angle and a radius to locate a point, while rectangular coordinates use x and y coordinates.

How do you find the area of a sector in polar coordinates?

To find the area of a sector in polar coordinates, you can use the formula A = 1/2 r²θ, where r is the radius and θ is the angle of the sector.

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