The relationship between rectangular coordinates (x, y) and polar coordinates [r, 0] can be described by the equations x = r cos 0, y = r sin 0 and with r = √√x² + y2, tan 8 = y/x. Use these equations to show that 2²r əx² 0²0 əx² = Ər əx 20 əx = cos 0, = (sin 0)² " sin 0 r 2 sin cos p² r 7 and 2²r dy² Ər ду 20 dy = = = sin 0 8²0 dy² cos r (cos 0)² r 2 sin cos ²
The relationship between rectangular coordinates (x, y) and polar coordinates [r, 0] can be described by the equations x = r cos 0, y = r sin 0 and with r = √√x² + y2, tan 8 = y/x. Use these equations to show that 2²r əx² 0²0 əx² = Ər əx 20 əx = cos 0, = (sin 0)² " sin 0 r 2 sin cos p² r 7 and 2²r dy² Ər ду 20 dy = = = sin 0 8²0 dy² cos r (cos 0)² r 2 sin cos ²
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The relationship between rectangular coordinates (x, y) and polar coordinates [r, 0] can be
described by the equations x = r cos 0, y = r sin 0 and with r = √√x² + y2, tan 8 = y/x.
Use these equations to show that
2²r
дх2
8²0
əx²
||
Ər
əx
20
əx
=
cos 0,
sin 0
(sin 0)²
r
2 sin cos
p2
r
and
2²r
მყ2
Ər
ду
=
20
ду
8²0
მყ2
sin 0
cos
(cos 0)²
r
=
r
2 sin cos
p2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d6184e7-845c-4f57-a052-7c2d18255cbe%2F0088904d-83f3-4d66-92a9-cd614beb6c19%2Fyfkzn9m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The relationship between rectangular coordinates (x, y) and polar coordinates [r, 0] can be
described by the equations x = r cos 0, y = r sin 0 and with r = √√x² + y2, tan 8 = y/x.
Use these equations to show that
2²r
дх2
8²0
əx²
||
Ər
əx
20
əx
=
cos 0,
sin 0
(sin 0)²
r
2 sin cos
p2
r
and
2²r
მყ2
Ər
ду
=
20
ду
8²0
მყ2
sin 0
cos
(cos 0)²
r
=
r
2 sin cos
p2
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