12. In the polar coordinate system, as defined in Chapter VIlc, r and e are related to x and y as r =x +y* and tane = ylx. a) Use the chain rule for differentiation to show that a sine a = cose- ax a, cose a r de and = sine ar r de dy dr b) Take the derivative of f(r,0) = rsin(20) in the Cartesian coordinate system.
12. In the polar coordinate system, as defined in Chapter VIlc, r and e are related to x and y as r =x +y* and tane = ylx. a) Use the chain rule for differentiation to show that a sine a = cose- ax a, cose a r de and = sine ar r de dy dr b) Take the derivative of f(r,0) = rsin(20) in the Cartesian coordinate system.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
Related questions
Question
12. In the polar
to x and y as r2 = x2 + y2 and tanθ = y/x. a) Use the chain rule for differentiation to
show that
∂/∂x = cosθ ∂/∂r + sinθ/r ∂/∂θ and ∂/∂y=sinθ ∂/∂r + cosθ/r ∂/∂θ
b) Take the derivative of f(r,θ) = rsin(2θ) in the Cartesian coordinate system.
Transcribed Image Text:12. In the polar coordinate system, as defined in Chapter VIlc, r and e are related
to x and y as r =x +y and tane = y/x. a) Use the chain rule for differentiation to
show that
a sine a
a, cose a
r de
= cose.
and
= sine
ax
ar
r de
ду
dr
b) Take the derivative of f(r,0) = rsin(20) in the Cartesian coordinate system.
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