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Parametric equations are a mathematical representation of a curve or surface in terms of one or more independent variables, known as parameters. They allow for more flexibility and freedom in representing complex shapes and movements compared to traditional Cartesian equations.
To graph parametric equations, you will need to plot the values of the dependent variables (x and y) for different values of the parameter. This will create a set of points, which can then be connected to form a curve or surface. You can also use a graphing calculator or online graphing tool to graph parametric equations.
The main difference between parametric equations and Cartesian equations is that parametric equations use parameters to define a curve or surface, while Cartesian equations use x and y coordinates. Parametric equations also allow for more complex and flexible representations, while Cartesian equations are more limited in their scope.
To convert parametric equations to Cartesian equations, you will need to eliminate the parameter by solving for it in terms of x or y. This will give you a relationship between x and y, which can then be expressed as a Cartesian equation.
Parametric equations have many real-life applications, such as in physics, engineering, and computer graphics. They are used to model the motion of objects, design curves and surfaces, and create realistic animations and special effects in movies and video games. They are also used in mathematical modeling and research to study complex systems and phenomena.
