   Chapter 10, Problem 16RE

Chapter
Section
Textbook Problem

# Sketch the polar curve.16. r = 3 2 − 2 cos θ

To determine

To sketch: The polar curve r=322cosθ.

Explanation

Given:

The Polar equation for the variable r is as follows.

r=322cosθ (1)

The given polar equation is of the form.

r=ed1±ecosθ (2)

Equation (2) becomes

r=321cosθ

Comparing equation (1) and (2) we get,

ed=32 and e=1

So d=32.

The equation of the directrix is y=32.

As eccentricity, e is 1 the conic is a parabola.

Determine the value of r.

Substitute the value of 10° for θ.

r=3(2(2×cos(10°)×π180))=98.73

Similarly, substitute till 360° for θ.

To draw the curve for the values of x and y.

Determine the value of x.

x=rcosθ

Substitute the value of 1 for r and 0° for θ.

x=98.73×cos0°=97.23

Determine the value of y:

y=rsinθ

Substitute the value of 1 for r and 0° for θ

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