What Alpha Value Encloses an Area of 1 in Polar Coordinates?

Thread starter _MNice_
Start date Oct 4, 2012
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Area Curve Polar

In summary, the formula for finding the area under a polar curve is A = 1/2 ∫a^b r^2 dθ, where a and b represent the starting and ending angles, and r is the distance from the origin to the curve at each angle. The area under a polar curve is different from the area under a cartesian curve because it involves integrating over the angle instead of the x-axis and takes into account multiple "loops". The negative area under a polar curve represents the area below the polar axis and is affected by the shape of the curve. Curves with more "loops" or larger distances from the origin will have a larger area, while curves with smaller distances or more compact shapes will have a smaller area

Oct 4, 2012

_MNice_

1. For what value of α is the area enclosed by r=∅, ∅=0, and ∅=α equal to 1?

2. x=rcos(∅)
y=rsin(∅)

3. x=∅cos(0)
x=∅cos(α)
y=∅sin(∅)
y=∅cos(α)

Don't know what to do after this

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Oct 4, 2012

LCKurtz

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There is no point nor any need for rectangular coordinates for this problem. What is the polar coordinate integral formula for area inside r = f(θ)?

FAQ: What Alpha Value Encloses an Area of 1 in Polar Coordinates?

What is the formula for finding the area under a polar curve?

The formula for finding the area under a polar curve is A = 1/2 ∫_a^b r² dθ, where a and b represent the starting and ending angles, and r is the distance from the origin to the curve at each angle.

How is the area under a polar curve different from the area under a cartesian curve?

The area under a polar curve is calculated using a different formula and involves integrating over the angle instead of the x-axis. Additionally, polar curves can have multiple "loops" and the area calculation takes this into account.

What is the significance of the negative area under a polar curve?

The negative area under a polar curve represents the area that is below the polar axis. This can occur when the curve crosses the polar axis multiple times or when the curve is entirely below the axis.

How does the shape of the polar curve affect the area calculation?

The shape of the polar curve can greatly affect the area calculation. Curves with more "loops" or larger distances from the origin will have a larger area, while curves with smaller distances or more compact shapes will have a smaller area.

Can the area under a polar curve be negative?

Yes, the area under a polar curve can be negative. This occurs when the curve crosses the polar axis multiple times or when the entire curve is below the axis. In these cases, the negative area represents the area that is below the polar axis.