Representing Cartesian coordinate curves using explicit and implicit forms. Representing curves using parametric equations which define x and y in terms of a third variable. Includes examples of parametric equations for a circle, ellipse, and projectile fired at an angle.

Finding implicit forms for parameterized curves. Uses examples from the previous section of the notes.

Definition, with examples of circles and a horizontal line defined in polar coordinates.

Using parametric equations to define a curve in two or three dimensions and properties of parametric equations.

Nine questions which involve finding equations in rectangular coordinates for those given in parametric form, or putting a rectangular equation in parametric form.

Solution (PDF - 4.0 MB)^# Pages 58 to 59

Three multi-part questions which involve converting rectangular coordinates to polar coordinates, converting polar equations to rectangular equations, and graphing curves given in polar coordinates.

Solution (PDF - 4.0 MB)^# Pages 62 to 63

Sketching a curve in polar coordinates, and labeling the quadrants, endpoints, tangent slopes, and angles for the curve.

Solution (PDF) Pages 3 to 4

Sketching a curve defined in polar coordinates and finding the area inside it.

Solution (PDF)^# Page 1

Sketching a curve given in polar coordinates and finding points of intersection between that and other curves.

Solution (PDF)^# Page 1

Representing a circle using both rectangular and polar coordinates.

Solution (PDF)^# Page 1

Setting up and evaluating an integral to represent the uncovered area of the two moons involved in a lunar eclipse on another planet.

Solution (PDF)^# Page 1

Sketching a spiral defined in polar coordinates, counting the times it crosses the x-axis, and finding the area of specific regions of the spiral.

Solution (PDF)^# Page 1

Finding an equation in polar coordinates and the appropriate range of theta for a line given in rectangular coordinates.

Solution (PDF)^# Page 1

Sketching a curve given in polar coordinates and finding the area swept by a line segment as one of the endpoints moves along this curve.

Solution (PDF)^# Page 1

Applet for showing the graph of a function defined in polar coordinates.

Applet for plotting curves defined in rectangular or parametric form.