   Chapter 10.3, Problem 55E

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.55. r = 2 cos θ, θ = π/3

To determine

To find: The slope of the tangent line for the polar curve r=2cosθ at the point θ=π3 .

Explanation

Given:

The slope of the tangent line for the polar curve is r=2cosθ .

Calculation:

Substitute (2cosθ) for r in equation x=rcosθ .

x=rcosθ=(2cosθ)cosθx=2cos2θ

Substitute (2cosθ) for r in equation y=rsinθ .

y=rsinθ=(2cosθ)sinθ=2cosθsinθ

Differentiate the equation x=2cos2θ with respect to θ .

x=2cos2θdxdθ=2×2cosθ(sinθ)

Differentiate the parametric equation y=2cosθsinθ with respect to θ .

y=2cosθsinθdydθ=2cos2θ

Write the chain rule for function dydx

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