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Find the Jacobian ∂(x,y) ∂(u,v) for the transformations x=4ucos(6v), y=4usin(6v) and x=4usin(6v), y=4ucos(6v).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 7RE

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Question

Find the Jacobian ∂(x,y) ∂(u,v) for the transformations x=4ucos(6v), y=4usin(6v) and x=4usin(6v), y=4ucos(6v).

a(x,y)
for the transformations x = 4u cos (6v), y = 4u sin (6v) and x = 4u sin (6v), y = 4u cos (6v).
d(u,v)
Find the Jacobian
The Jacobian for x = 4u cos (6v), y = 4u sin (6v) is
96
The Jacobian for x = 4u sin (6v), y = 4u cos (6v) is

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