Converting Cartesian to Polar Coordinates: How Do We Get r and Theta?

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Homework Help Overview

The discussion revolves around converting a linear equation from Cartesian coordinates to polar coordinates, specifically the equation y = 3x + 4. Participants are exploring how to express this equation in terms of the polar variables r and theta.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • One participant attempts to manipulate the equation by squaring both sides but encounters difficulty. Others suggest substituting the polar forms of x and y directly into the equation to simplify the conversion process.

Discussion Status

Participants are actively discussing different methods for converting the equation, with some providing guidance on substitution techniques. There is a focus on ensuring the final expression isolates r in terms of theta, although no consensus has been reached on the best approach yet.

Contextual Notes

There is an emphasis on the goal of obtaining a function that expresses r solely in terms of theta, which may influence the methods discussed. The original poster's progress indicates a potential gap in understanding the substitution process.

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Homework Statement


Write equation in polar form. y=3x+4


Homework Equations


x^2 + y^2 = r^2
x = rcos(theta)
y = rsin(theta)
tan(theta) = y/x


The Attempt at a Solution



Square both sides...
y^2 = 9x^2 + 24x + 16

r^2 - x^2 = 9x^2 +24x +16

r^2 = 10x^2 + 24x + 16

And that's where I got stuck...
 
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Don't do it like that. Substitute the polar form of x and y into your equation... and you'll be done.
 
Replace EVERY x with [itex]r cos(\thet[/itex] and EVERY y with [itex]r sin(\theta)[/itex]
 
What is your goal in converting from Cartesian to polar coordinates? You want to get a function that is:
r = a bunch of theta junk

So how do we turn y=3x+4 into an equation of nothing but r’s and theta’s? We use the two substations you have, then we get r all by it self on one side.
 

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