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Give equations describing the regions below in cylindrical or spherical coordinates. (a) The unit circle in the yz-plane; that is, the circle satisfying y² + z² = 1 and x = 0. (Use spherical coordinates.) (b) The region whose definition in rectangular coordinates is {(x, y, z) = R³ : x² + y² = z² and 0 ≤ z ≤ 1}. (Use cylindrical coordinates.) (c) The bottom half of a solid sphere of radius 2 centered at the origin. (Use spherical coordinates.) (d) The same region as in part (c), but use cylindrical coordinates this time.

Give equations describing the regions below in cylindrical or spherical coordinates. (a) The unit circle in the yz-plane; that is, the circle satisfying y² + z² = 1 and x = 0. (Use spherical coordinates.) (b) The region whose definition in rectangular coordinates is {(x, y, z) = R³ : x² + y² = z² and 0 ≤ z ≤ 1}. (Use cylindrical coordinates.) (c) The bottom half of a solid sphere of radius 2 centered at the origin. (Use spherical coordinates.) (d) The same region as in part (c), but use cylindrical coordinates this time.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 43E
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Give equations describing the regions below in cylindrical or spherical coordinates.
(a) The unit circle in the yz-plane; that is, the circle satisfying y^2 + z^2 = 1 and x = 0. (Use spherical coordinates.)
(b) The region whose definition in rectangular coordinates is
{(x, y, z) ∈ R3: x^2 + y^2 = z^2 and 0 ≤ z ≤ 1}.
(Use cylindrical coordinates.)
(c) The bottom half of a solid sphere of radius 2 centered at the origin. (Use spherical
coordinates.)
(d) The same region as in part (c), but use cylindrical coordinates this time.

Give equations describing the regions below in cylindrical or spherical coordinates. (a) The unit circle in the yz-plane; that is, the circle satisfying y² + z² = 1 and x = 0. (Use spherical coordinates.) (b) The region whose definition in rectangular coordinates is {(x, y, z) = R³ : x² + y² = z² and 0 ≤ z ≤ 1}. (Use cylindrical coordinates.) (c) The bottom half of a solid sphere of radius 2 centered at the origin. (Use spherical coordinates.) (d) The same region as in part (c), but use cylindrical coordinates this time.
Transcribed Image Text:Give equations describing the regions below in cylindrical or spherical coordinates. (a) The unit circle in the yz-plane; that is, the circle satisfying y² + z² = 1 and x = 0. (Use spherical coordinates.) (b) The region whose definition in rectangular coordinates is {(x, y, z) = R³ : x² + y² = z² and 0 ≤ z ≤ 1}. (Use cylindrical coordinates.) (c) The bottom half of a solid sphere of radius 2 centered at the origin. (Use spherical coordinates.) (d) The same region as in part (c), but use cylindrical coordinates this time.
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