Polar Coordinates

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Polar Coordinates

• Review
• Cartesian (or rectangular) coordinates are
  convenient for
• Measuring distance from a point to the x or y
  axes
• Translations

However, it is inconvenient for rotations and
measuring distances from the origin to a given
point.
In some applications, we are more interested in
the distance from the origin to a given point and
also the direction of that given point relative
to the x-axis, therefore we need to create a new
type of coordinates for those applications. For
example, the air traffic controllers in a busy
airport need to know how far the planes are from
the airport and from which directions they are
coming in.
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Conversion from Polar to Cartesian
Conversion from Cartesian to Polar
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Disadvantages of the Polar Coordinates 1. The
coordinates of a given point is never unique
because the radius can be positive or negative,
and the angle ? can be bigger than 360 2. At the
Pole, the angle ? is undefined.
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Polar Curves
In polar coordinates, it is usually more
convenient to express the radius r as a function
of the angle ?, i.e.
r f (?)

• Example
• r 5 will produce a circle of radius 5
  centered at the origin.
• r ? will produce a spiral starting at the
  Pole.

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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?
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Polar Curve r 0.5 cos ?