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Chapter 9: Q. 7 (page 630)

The variables r and u represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x, y). (b) Identify the equation and graph it.

r=2sin胃

Short Answer

Expert verified

The polar equation as an equation in rectangular coordinates isx2+(y-1)2=1

Step by step solution

01

Step 1. Given data

r=2sin胃

02

Step 2. Multiply both sides of the given equation by r. 

r脳r=r脳2sin胃

r2=2rsin胃

03

Step 3. Substitute r2=x2+y2 and y for r sinθ in above equation

x2+y2=2y

x2+y2-2y=0

04

Step 4. Adding 1 on both the sides of the equation

x2+y2-2y+1=1

x2+(y2-2y+1)=1

x2+(y-1)2=1

Above equation is in the form of rectangular coordinate system with center (0,1) and radius 1.

05

Step 5. draw the graph

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