Finding Points of Intersection for Polar Curves

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Homework Help Overview

The discussion revolves around finding the points of intersection for two polar curves, specifically focusing on identifying these points in polar coordinates.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting the polar equations equal to each other and simplifying to find intersection points. There is mention of using trigonometric identities to solve for angles and substituting back to find corresponding polar coordinates.

Discussion Status

Some participants have provided guidance on identifying one intersection point and are exploring how to find the second point. There is an ongoing inquiry into the values of θ that satisfy the equations, with no explicit consensus reached on the complete solution.

Contextual Notes

Participants are considering the periodic nature of the tangent function and its implications for finding multiple intersection points. The original poster has noted the origin as one intersection point but is seeking confirmation and additional points.

jjeddy
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Homework Statement


I need to find the 2 points of intersection (in polar form) of the two curves.

I know just by looking that the origin will be one of the points, (0,0)

The Attempt at a Solution



I have approached this two different ways,

1. set them equal to each other and tried to simplify.Which approach should i use?
 
Last edited:
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OK, i used tanθ=sinθ/cosθ and i solved for θ

i can substitute back into get my corresponding (r,θ) r point and i should have my point right?
 
Last edited:
Right. That gives you one of the points. I'm not quite sure how you came up with your answer of θ=π/4 , so it's difficult to suggest how you should come up with the second point.
 
Is that right?I think that is my polar coordinate where it intersects
 
Last edited:
Your first post states that you need to find the 2 points of intersection.

For what other value of θ, is tan(θ) = 1 ? What is the period of the tangent function?
 

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