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- https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/07%3A_Parametric_Equations_and_Polar_Coordinates/7.02%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_222_Calculus_2/06%3A_Parametric_Equations_and_Polar_Coordinates/6.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/05%3A_Differential_Calculus_with_Parametric_Curves/5.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/10%3A_Parametric_Equations_and_Polar_Coordinates/10.02%3A_Parametric_EquationsThis section introduces parametric equations, where two separate equations define x and y as functions of a third variable, usually t. It explains how to graph parametric curves, eliminate...This section introduces parametric equations, where two separate equations define x and y as functions of a third variable, usually t. It explains how to graph parametric curves, eliminate the parameter to find Cartesian equations, and analyze motion along a path. Examples illustrate the flexibility of parametric equations in describing curves that are difficult to express in standard Cartesian form.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/05%3A_Parametric_Equations_and_Polar_Coordinates/5.01%3A_Parametric_EquationsThis section introduces parametric equations, where two separate equations define x and y as functions of a third variable, usually t. It explains how to graph parametric curves, eliminate...This section introduces parametric equations, where two separate equations define x and y as functions of a third variable, usually t. It explains how to graph parametric curves, eliminate the parameter to find Cartesian equations, and analyze motion along a path. Examples illustrate the flexibility of parametric equations in describing curves that are difficult to express in standard Cartesian form.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/11%3A_Parametric_Equations_and_Polar_Coordinates/11.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/06%3A_Parametric_Equations_and_Polar_Coordinates/6.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_II_(Reed)/11%3A_Parametric_Equations_and_Polar_Coordinates/11.02%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/09%3A_Curves_in_the_Plane/9.02%3A_Parametric_EquationsThe rectangular equation y=f(x)y=f(x) works well for some shapes like a parabola with a vertical axis of symmetry, but in the previous section we encountered several shapes that could not be sketche...The rectangular equation y=f(x)y=f(x) works well for some shapes like a parabola with a vertical axis of symmetry, but in the previous section we encountered several shapes that could not be sketched in this manner. (To plot an ellipse using the above procedure, we need to plot the "top'' and "bottom'' separately.) In this section we introduce a new sketching procedure.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/04%3A_Parametric_Equations/4.01%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q3/03%3A_Parametric_Equations_and_Polar_Coordinates/3.02%3A_Parametric_EquationsIn this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.