Define a circle tangent to the -axis by:

Sketch this graph in polar coordinates and compute the area of the radial set.

The sketch is as follows:

Then, we compute the area,

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Stumbling Robot

A Fraction of a Dot
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Tag: Polar Coordinates

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Sketch a circle tangent to the y-axis and compute its area from -π/2 to π/2

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Sketch the Spiral of Archimedes and compute its area from 0 to 2 π

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Show an equivalence between given sets in Cartesian and polar coordinates

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Show an equivalence between given sets in Cartesian and polar coordinates

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Show an equivalence between given sets in Cartesian and polar coordinates

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Show an equivalence between given sets in Cartesian and polar coordinates

Define a circle tangent to the -axis by:

Sketch this graph in polar coordinates and compute the area of the radial set.

The sketch is as follows:

Then, we compute the area,

Define

* Spiral of Archimedes: * for .

Sketch this graph in polar coordinates and compute the area of the radial set.

The sketch is as follows:

Then, we compute the area,

Show that the sets of points satisfying

are equal.

Letting and we plug in to the given Cartesian equation,

Show that the sets of points satisfying

are equal.

Letting and we plug in to the given Cartesian equation,

Show that the sets of points satisfying

are equal.

Letting and we plug in to the given Cartesian equation,

Show that the sets of points satisfying

are equal.

Letting and we plug in to the given Cartesian equation,

where so (hence, we can divide by ) in the second to last line.