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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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