Curve on a Spherical Surface
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Hi
I have this curve C defined by x=sin(2t), y=1-cos(2t), z=2cos(t) where t lies between (or equal to) -pi and pi.
How do I show that this curve lies on a spherical surface with central in origon and radius = 2?
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Solution Summary
It is proven that a curve lies on a spherical surface.
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Proof:
From the condition, we have
x^2 + y^2 + z^2 = (sin(2t))^2 + (1 - cos(2t))^2 + (2cos(t))^2
= (sin(2t))^2 + 1 + ...
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