I got this HW question made up by the professor that I find ambiguous. It says(adsbygoogle = window.adsbygoogle || []).push({});

Consider the curve [itex]\theta (t)=\pi/2-t[/itex], [itex]\phi(t)=\log \cot(\pi/4-t/2)[/itex] on the sphere [itex]r(\theta,\phi)=(\sin\theta \cos\phi,\sin\theta\sin\phi,cos\theta)[/itex]

Find the lenght of the curve btw the points t=pi/6 and pi/4

He did not specify domains for either the curve nor the "surface" r. On one hand, if we take r to be a surface patch, this requires that the (maximum) domain be [itex]0 < \theta < \pi[/itex], [itex] 0 < \phi < 2\pi[/itex]. Anything bigger and the domain is not open or r is not injective. But this surface patch does not cover thewholesphere.

I could also consider two other surface patches of the form [itex]r_{2,3}(\theta,\phi)=(\sin\theta \cos\phi,\sin\theta\sin\phi,cos\theta)[/itex] with appropriate domains, that together with r above form an atlas for the unit sphere.

Any thoughts? How would you interpret this question?

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# Homework Help: How should I interpret?

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