Question

How do I find the trace of the curve (e^(-t) cos t , e^(-t) sin t))? I know that if it was simply (cos t, sin t), that it would be a circle of equation x^2 + y^2 = 1, but I don't know how to account for the deformation the e^(-t) is going to cause.

Answer 1

i think its like a circle but the radius is decreasing

Answer 2

Thank you!

Answer 3

do you understand why ?

Answer 4

I am going to make a graph, I think it's because of the 1/e^t, e^t gets greater and so 1/e^t gets smaller and smaller.