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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 52RE

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5. u is defined on {(r, y)|x² +y} s 1} and u+uy =0 where u=2(x+y)% on
{(r, y)|r² + f = 1}. Find u as a polynomial in r, y.
00
Hint 1: In polar coordinates, u(r, 6)=q,+E [4"cos(n®)+b,r" sin(n6)] where
n=1
an, b, are the Fourier coefficients of f(8) :=u(1,0).
Hint 2: cos(30)= 4(cos 0)³ – 3cos 0, sin(30)=3 sin 0 – 4(sin0)³.

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