What is the equation for the given curve in polar coordinates?

AI Thread Summary
The discussion focuses on converting the parametric equations x = e^Kcos(k) and y = e^Ksin(k) into polar coordinates. The key transformation results in the equation r = e^k, where r represents the radial distance and k is the angle. The participant clarifies that the relationship between x, y, and r leads to the conclusion that r^2 = e^(2k). The final answer, r = e^k, accurately describes the curve in polar coordinates, maintaining consistency with the original parametric forms. This conversion effectively captures the essence of the curve defined by the initial equations.
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Homework Statement



x = eKcos(k)
y=eKsin(k)

-∞ < K < ∞

Find an equation in polar coordinates for the above curve


The Attempt at a Solution



I am not fully clear as to what the question is asking.

If its asking for (r,k), where K is normally a theta value then it would be (e^k,k)

other than that,

x^2+y^2=e^2k

r^2 = e^2k

r = √e^2k = e^k

---

Any help or suggestions would be appreciated!
 
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r = ek is the answer you're looking for. It's an equation in polar coordinates and spans the same curve as your original parametric equations.
 

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