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Chapter 9: Q. 2 (page 629)

In Problems 1鈥�3, plot each point given in polar coordinates, and find its rectangular coordinates:

-2,4蟺3

Short Answer

Expert verified

The rectangular co-ordinates of the polar co-ordinate -2,4蟺3are (1,3)and the graph is

Step by step solution

01

Step 1. Given Information 

We are given the polar co-ordinates as-2,4蟺3

Comparing it with standard polar co-ordinates (r,胃), we get,

r=-2胃=-4蟺3

02

Step 2. Plotting the polar co-ordinate 

Since the angle is 4蟺3, we will make the angle between the axis and the line as 4蟺3Also the length is given as r=-2(Opposite direction)

Therefore, the graph will look like,

03

Step 3. Rectangular co-ordinates. 

We know, the relation between polar and rectangular co-ordinates is,

x=rcos胃andy=rsin胃

Thus, the value of,

x=rcos胃=-2路cos4蟺3=-2路-12=1y=rsin胃=-2路sin4蟺3=-2路-32=3

The co-ordinate will be(1,3)

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