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Analogue of spherical coordinates in $n$-dimensions

If we take a 2-sphere of radius a, we can define $ f(z, t) = (\sqrt{a^2-z^2}\cos t,\sqrt{a^2-z^2}\sin t, z) $ it's a parametrization of the sphere, if $ 0 < t < 2\pi $ and $ |z| < a $. Also, it's a coordinate patch covering it. Is it possible to write down such a function for a general n-sphere?

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Ormi
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    Let $z = a\cos\theta$ and $\sqrt{a^2-z^2} = a\sin\theta$, and what you're describing is spherical coordinates. Then your question becomes a duplicate of this one. :) –  Nov 15 '12 at 21:56
  • Oh, thanks a lot Rahul! :) – Ormi Nov 15 '12 at 22:03

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