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Find the parametric representation for the surface:
The part of the sphere x^2 + y^2 +z^2 = 4 that lies above the cone z= sqrt(x^2 + y^2).
 2 years ago
 2 years ago
Find the parametric representation for the surface: The part of the sphere x^2 + y^2 +z^2 = 4 that lies above the cone z= sqrt(x^2 + y^2).
 2 years ago
 2 years ago

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Mr.MathBest ResponseYou've already chosen the best response.0
You can use spherical coordinates.
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.0
\[x=2\sin\phi \cos\theta\] \[y=2\sin\phi\sin\theta\] \[z=2\cos\phi\] \[0\le \phi\le \pi \text{ and } 0\le \theta \le \pi\]
 2 years ago

malevolence19Best ResponseYou've already chosen the best response.0
Mr. Math, I have to ask, would you not use: \[x=2\sin(\phi)\cos(\theta); y=2\sin(\phi)\sin(\theta); z=2\cos(\phi); 0 \le \phi \le \frac{\pi}{4}; 0 \le \theta \le 2 \pi\] Because the cone creates a 45 degree angle in the first quadrant of the xy plane. So the phi angle (defined from the positive xaxis would only go down TO THE CONE, not the entire pi which would give you the whole sphere. It says above the cone, so would it be to pi/4?
 2 years ago
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