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Chapter 6: Problem 67

Writing Write a short paragraph explaining why parametric equations are useful.

Short Answer

Expert verified
Parametric equations are a valuable mathematical tool used to express a relationship among several variables that are dependent on a parameter. They prove to be useful in several fields such as physics, computer graphics, engineering, among others, for aiding in tasks such as representing motion in dimensions, modeling objects, curve fitting, among others.

Step by step solution

01

Definition of Parametric Equations

Parametric equations are a set of equations that express the coordinates of points in the Cartesian plane, in terms of a single parameter. Typically, this parameter is time (denoted as t) or another variable.
02

Benefits of Using Parametric Equations

One of the main benefits of using parametric equations is that they allow us to express a relationship between two variables that are dependent on a third variable. This is used widely in different disciplines; in physics, they are used to represent motion in two or three dimensions, in computer graphics, they're used to model objects in 2D and 3D space, in engineering, they're used in curve fitting and computer-aided design.
03

Conclusion to the Utility of Parametric Equations

Overall, parametric equations bring about an enormous facility when dealing with complex scenarios in many areas of study. Their ability to simplify and clarify the relationship among variables depending on a parameter turned them into a valuable tool in mathematical applications.

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Most popular questions from this chapter

In Exercises 7-12, test for symmetry with respect to \(\theta=\pi / 2\), the polar axis, and the pole. \(r=5+4 \cos \theta\)

\(r=\cos 2 \theta\)

\(r=4+3 \cos \theta\)

In Exercises 33-48, find a polar equation of the conic with its focus at the pole. $$ \begin{array}{ll} {\text { Conic }} & \text { Vertex or Vertices } \\ \text { Parabola } & (5, \pi) \\ \end{array} $$

\(r=\frac{2}{1+\sin \theta}\)
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