Trigonometry Series - Concepts and Formulas™
Parametric Representations of Curves (TRG-CF9)
This sheet provides a comprehensive review of all of the most important topics, concepts and formulas covering using parametric equations to represent curves. Each concept is explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas™ sheet answers questions about how to use the concepts - how to actually solve problems with them, it doesn't just list facts and formulas.

Topics Covered:

• Representations of curves
• Parametric representations of curves
• Sketching parametric curves
• How to eliminate the parameter
• Lines in parametric form
• Parabolas in parametric form
• Circles in parametric form
• Ellipses in parametric form
• Hyperbolas in parametric form
• Hypocycloids, cycloids and astroids in parametric form
• How to convert a rectangular equation to parametric form
• Some common curves and their parametric representations
• Polar coordinate systems
• The polar origin
• Directed distances and angles
• The relationship between polar and rectangular coordinates
• How to convert points between polar and rectangular coordinates
• Polar equations
• How to convert equations between polar and rectangular coordinates
• Graphing polar equations
• Symmetries of polar graphs
• General polar equations of lines
• General polar equations of parabolas
• General polar equations of circles
• General polar equations of hyperbolas
• General polar equations of cardioids
• General polar equations of limaçons
• General polar equations of roses
• General polar equations of spirals