anonymous
  • anonymous
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).
Mathematics
katieb
  • katieb
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Mr.Math
  • Mr.Math
You can use spherical coordinates.
Mr.Math
  • Mr.Math
\[x=2\sin\phi \cos\theta\] \[y=2\sin\phi\sin\theta\] \[z=2\cos\phi\] \[0\le \phi\le \pi \text{ and } 0\le \theta \le \pi\]
anonymous
  • anonymous
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 x-y plane. So the phi angle (defined from the positive x-axis 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?

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