   Chapter 10.3, Problem 44E

Chapter
Section
Textbook Problem

Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.44. r2θ = 1

To determine

To sketch: The curves for the polar equation r2θ=1 and its Cartesian coordinates.

Explanation

Given:

The polar equation is r2θ=1.

Calculation:

Substitute (0.0873) for θ in equation r=1θ,

r2=1(0.0873)=10.0873=3.38

Substitute (0.0873) for θ in equation r=1θ,

r2=1(0.0873)=10.0873=3.38

For the polar equation r=1θ the values for the Cartesian coordinates curve is tabulated below.

 θ (degrees) θ (rad) r 5 0.087305556 3.384379532 35 0.611138889 1.279175226 65 1.134972222 0.938657995 95 1.658805556 0.776429914 125 2.182638889 0.676875906

For the polar equation r=1θ the values for the Cartesian coordinates curve is tabulated below.

 θ (degrees) θ (rad) r 5 0

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