1 3. Find parameterizations of the following surfaces: (a) The rectangle with corners (1, 0, 0), (1, 0, 1), (0, 1, 0), and (0, 1, 1). (b) The portion of the sphere x² + y² + z² = 1 with x ≥ 0. (c) The portion of the cone with equation x² + y² = 22 bounded by 1 ≤ z ≤ 3.

Trigonometry (MindTap Course List)
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Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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3. Find parameterizations of the following surfaces:
(a) The rectangle with corners (1, 0, 0), (1, 0, 1), (0, 1,0), and (0, 1, 1).
(b) The portion of the sphere x² + y² + z² = 1 with x ≥ 0.
(c) The portion of the cone with equation x² + y² = 22 bounded by 1 ≤ z ≤ 3.
Transcribed Image Text:1 3. Find parameterizations of the following surfaces: (a) The rectangle with corners (1, 0, 0), (1, 0, 1), (0, 1,0), and (0, 1, 1). (b) The portion of the sphere x² + y² + z² = 1 with x ≥ 0. (c) The portion of the cone with equation x² + y² = 22 bounded by 1 ≤ z ≤ 3.
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