   Chapter 10.4, Problem 35E

Chapter
Section
Textbook Problem

# Polar-to-Rectangular Conversion In Exercises 35-44, convert the polar equation to rectangular form and sketch its graph. r = 3 sin θ

To determine

To calculate:

The rectangular equation by the polar equation r=3sinθ and then sketch its graph.

Explanation

Formula Used:

The formula is x=rcosθ,y=rsinθ and r=x2+y2

Calculation:

As it is known that polar coordinates (r,θ) of a point are related to the rectangular coordinates (x,y) of point as follows:

x=rcosθ,y=rsinθ and r=x2+y2

Multiply r to both sides in the above polar equation r=3sinθ,

r2=3rsinθ

Substitute r2=x2+y2 and rsinθ=y in the above polar equation,

x2+y2=3y

x2+y23y=0

Rewrite the equation as standard form of circle equation by completing the square method,

Therefore, complete the square in equation by adding the term (b2)2=(32)2=94 in both sides in above rectangular equation,

x2+y23y+94=94

x2+y22

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