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{image} {image} {image} {image}

1. 2. 3. 4. Find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0. {image}. {image} {image} {image} {image}. 1. 2. 3. 4.

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{image} {image} {image} {image}

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  1. 1. 2. 3. 4. Find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0. {image} • {image} • {image} • {image} • {image}

  2. 1. 2. 3. 4. The Cartesian coordinates of a point are given. Find polar coordinates {image} of the point, where r < 0 and {image} {image} • {image} • {image} • {image} • {image}

  3. 1. 2. 3. 4. Sketch the curve with the given equation. {image} • {applet} • {applet} • {applet} • {applet}

  4. 1. 2. 3. 4. Sketch the curve with the given equation. {image} • {applet} • {applet} • {applet} • {applet}

  5. 1. 2. 3. 4. Sketch the curve with the given equation. {image} • {applet} • {applet} • {applet} • {applet}

  6. 1. 2. 3. The astronomer Giovanni Cassini (1625-1712) studied the family of curves with polar equations {image} where a and c are positive real numbers. These curves are called the ovals of Cassini even though they are oval shaped only for certain values of a and c. (Cassini thought that these curves might represent planetary orbits better than Kepler's ellipses.) Investigate the variety of shapes that these curves may have. In particular, how are a and c related to each other when the curve splits into two parts? {image} • {applet} • {applet} • {applet}

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