Finding Points of Intersection for Polar Curves

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To find the points of intersection for the given polar curves, one point is identified at the origin (0,0). The approach involves setting the curves equal and solving for θ using the tangent function. The discussion highlights the need to identify another value of θ where tan(θ) equals 1, considering the periodic nature of the tangent function. This leads to the conclusion that there are multiple angles that yield the same intersection point. The key takeaway is that both points of intersection can be derived from the periodicity of the tangent function.
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?
 
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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?
 
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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
 
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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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