   Chapter 10.3, Problem 58E

Chapter
Section
Textbook Problem

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.58. r = cos(θ/3), θ = π

To determine

To find: The slope of the tangent line for the polar curve r=cos(θ3) at the point θ=π .

Explanation

Given:

The slope of the tangent line for the polar curve r=cos(θ3) .

Calculation:

Differentiate the curve equation r with respect to θ .

r=cos(θ3)drdθ=13sin(θ3)

Write the chain rule for dydx .

dydx=dydθdxdθ = drdθsinθ+rcosθdrdθcosθrsinθ

Substitute [13sin(θ3)] for (drdθ) and [cos(θ3)] for (r) in equation (drdθsinθ+rcosθdrdθcosθrsinθ) .

dydx=drdθsinθ+rcosθdrdθcosθrsinθ=(13sin(θ3))sinθ+cos(θ3)cosθ(13sin(θ3))cosθcos(θ3)sinθ

The slope of the tangent line for the polar curve r=1θ at the point θ=π

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