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rcmango
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Homework Statement
Prove that the curve x = t cos(t), y = (pi/2 - t) sin(t) has a self-intersection at the point (0,0)
Homework Equations
The Attempt at a Solution
not sure where to start with this one. Please help.
To prove self-intersection at (0,0), we can use the concept of limit. We will take the limit of the functions as t approaches 0 from both the positive and negative sides. If the limit on both sides is equal to (0,0), then we can conclude that the functions intersect at (0,0).
The point (0,0) is significant because it is the origin, where the x and y axes intersect. It is also the starting point for the parametric equations given, and therefore, determining if there is self-intersection at this point is crucial.
Self-intersection means that the functions intersect with themselves at a particular point. In other words, there are two different values of t that result in the same (x,y) coordinates, indicating that the functions overlap or cross each other.
When there is self-intersection, the graph of the functions will have an overlapping or crossing point at (0,0). This will result in a loop or a cusp shape in the graph, indicating that the functions are intersecting with themselves at the origin.
Yes, it is possible for the functions to have self-intersection at a point other than (0,0). This can happen if the limit of the functions at that particular point is equal to that point. However, for the given functions, we are specifically trying to prove self-intersection at (0,0).