Parametric Equations for Circle and Spiral Curves

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SUMMARY

Parametric equations are mathematical representations that express the coordinates of points on curves as functions of a variable, typically denoted as 't'. In the discussion, the parametric representation of a circle defined by the equation y² + 4y + z² = 5 and x = 3 is explored. The specific parametric equations provided are x(t) = 3, y(t) = -2 + r cos(4t), and z(t) = 6 + r sin(4t), where 'r' is a constant that defines the radius. These equations describe a circular path in a three-dimensional space.

PREREQUISITES
  • Understanding of multivariable calculus concepts
  • Familiarity with parametric equations and their applications
  • Knowledge of trigonometric functions and their properties
  • Basic skills in manipulating algebraic equations
NEXT STEPS
  • Study the derivation of parametric equations for different geometric shapes
  • Learn about the applications of parametric equations in physics and engineering
  • Explore the use of parametric equations in computer graphics
  • Investigate the relationship between parametric equations and polar coordinates
USEFUL FOR

Students in multivariable calculus, educators teaching geometry, and professionals in fields such as physics and computer graphics who require a solid understanding of parametric equations.

mattb8818
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I was wondering if someone could give me an overview of what they are and how to get them. Thanks
 
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That is much too general a question. There are even many differents kinds of "parametric representation".
 
Ok, It is for a multivariable calcul us class. Could I give a few examples and maybe you could explain them to me?

Find parametric rep. of Circle y^2 + 4y + z^2 = 5, x = 3

what curves are represented?

2 + r cos 4t, 6 + r sin 4t, 2t
 

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