Converting Cartesian Coordinates to Cylindrical Coordinates

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SUMMARY

The discussion focuses on converting Cartesian coordinates to cylindrical coordinates, specifically addressing the line equation y = -5 and the point (0, -5). The key equations involved are y = r sin(φ) and x = r cos(φ). To convert Cartesian coordinates (x, y) to cylindrical coordinates (r, φ), one can derive r and φ by manipulating these equations, including squaring and adding them to eliminate variables.

PREREQUISITES
  • Understanding of Cartesian coordinates and their representation
  • Familiarity with cylindrical coordinates and their components
  • Knowledge of trigonometric functions and their relationships
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the conversion formulas between Cartesian and cylindrical coordinates
  • Learn how to derive r and φ from given x and y values
  • Explore the geometric interpretation of cylindrical coordinates
  • Practice converting various points and lines from Cartesian to cylindrical coordinates
USEFUL FOR

Students studying mathematics, particularly those focusing on coordinate systems, as well as educators teaching geometry and trigonometry concepts.

seang
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Homework Statement



Say I have line, y = - 5 in cartesian coordinates. How do I express this in cylindrical coordinates?

Also, if I have a point (0,-5) in cartesian coordinates, how to I express this position vector in cylindrical coordinates?

Homework Equations



y = r sin (phi)

j = r(hat)cos (phi) - phi(hat) sin (phi)


The Attempt at a Solution



THe relations are right there but I've forgotten howto use them.
 
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do you remember how to turn say (x,y) into (r,\theta) in 2D? the idea there is similar...
 
Cylindrical coordinates? That's in 3d but you only mention 2 coordinates? Perhaps you mean polar coordinates- cylindrical coordinates but ignore the z component.

You mention y= r sin(\phi) (I would have used \theta). Do you also know that x= r cos(\phi)? Solve those two equations for r and \phi in terms of x and y. The first is easy! You can eliminate \phi by squaring both equations and adding. The second is about as easy: eliminate r by dividing one equation by the other.
 

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