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Chapter 9: Q. 47 (page 568)

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

(-1,-蟺3)

Short Answer

Expert verified

The rectangular coordinates corresponding to the polar coordinates (-1,-蟺3)are (-12,32).

Step by step solution

01

Step 1. Given information

The given poplar coordinates of a point(-1,-蟺3)

02

Step 2. Finding the value of x.

For a point P on the terminal side of 胃and having polar coordinates (r,胃), the corresponding rectangular coordinates are given by x=rcos胃andy=rsin胃.
Substitute -1 for 1 and -蟺3for 胃in x=rcos胃 to get the value of x.

x=rcos胃=-1.cos(-蟺3)=-1.12=-12

03

Step 3. Finding the value of y.

Substitute -1 for r and -蟺3for 胃in to get the value of y.
y=rsin胃=-1.sin(-蟺3)=-1.-sin(蟺3)=-1.(-32)=32
Therefore, the rectangular coordinates corresponding to the polar coordinates(-1,-蟺3)are(-12,32).

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