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Parametrized Surfaces Just as you describe curves in the plane parametrically with a pair of equations x = f(t), y = g(f) defined on some parameter interval I, you can sometimes describe surfaces in space with a triple of equations x = f(u, v), y = g(u, v), z = h(u, v) defined on some parameter rectangle a < us b, c < v s d. Many computer algebra systems permit you to plot such surfaces in para- metric mode. (Parametrized surfaces are discussed in detail in Section 16.5.) Use a CAS to plot the surfaces in Exercises 77-80. Also plot several level curves in the xy-plane. 77. x = u cos v, y = u sin v, z = u, 0

Parametrized Surfaces Just as you describe curves in the plane parametrically with a pair of equations x = f(t), y = g(f) defined on some parameter interval I, you can sometimes describe surfaces in space with a triple of equations x = f(u, v), y = g(u, v), z = h(u, v) defined on some parameter rectangle a < us b, c < v s d. Many computer algebra systems permit you to plot such surfaces in para- metric mode. (Parametrized surfaces are discussed in detail in Section 16.5.) Use a CAS to plot the surfaces in Exercises 77-80. Also plot several level curves in the xy-plane. 77. x = u cos v, y = u sin v, z = u, 0

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
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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Parametrized Surfaces

Parametrized Surfaces Just as you describe curves in the plane parametrically with a pair of equations x = f(t), y = g(f) defined on some parameter interval I, you can sometimes describe surfaces in space with a triple of equations x = f(u, v), y = g(u, v), z = h(u, v) defined on some parameter rectangle a < us b, c < v s d. Many computer algebra systems permit you to plot such surfaces in para- metric mode. (Parametrized surfaces are discussed in detail in Section 16.5.) Use a CAS to plot the surfaces in Exercises 77-80. Also plot several level curves in the xy-plane. 77. x = u cos v, y = u sin v, z = u, 0<u s 2, 0 sv< 27 78. x = u cos v, y = u sin v, z = v, 0 us 2, 0 <v< 27 79. x = (2 + cos u) cos v, y = (2 + cos u) sin v, z = sin u, 0 sus 27, 0 s v< 27 80. x = 2 cos u cos v, y = 2 cos u sin v, z = 2 sin u, 0=u= 2π, 0υ π
Transcribed Image Text:Parametrized Surfaces Just as you describe curves in the plane parametrically with a pair of equations x = f(t), y = g(f) defined on some parameter interval I, you can sometimes describe surfaces in space with a triple of equations x = f(u, v), y = g(u, v), z = h(u, v) defined on some parameter rectangle a < us b, c < v s d. Many computer algebra systems permit you to plot such surfaces in para- metric mode. (Parametrized surfaces are discussed in detail in Section 16.5.) Use a CAS to plot the surfaces in Exercises 77-80. Also plot several level curves in the xy-plane. 77. x = u cos v, y = u sin v, z = u, 0<u s 2, 0 sv< 27 78. x = u cos v, y = u sin v, z = v, 0 us 2, 0 <v< 27 79. x = (2 + cos u) cos v, y = (2 + cos u) sin v, z = sin u, 0 sus 27, 0 s v< 27 80. x = 2 cos u cos v, y = 2 cos u sin v, z = 2 sin u, 0=u= 2π, 0υ π
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