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Chapter 9: Q. 58 (page 568)

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

0,-2

Short Answer

Expert verified

The polar coordinates is 2,-蟺2.

Step by step solution

01

Step 1. Given Information  

We are given rectangular coordinates of a point,

0,-2

We have to find polar coordinates of given point.

02

Step 2. Finding the polar coordinates  

The point (0,-2)lies in the third quadrant, so

x=rcos胃rcos胃=0-(1)y=rsin胃rsin胃=-2-(2)

Squaring both side and adding the two equations, we get

(rcos胃)2+(rsin胃)2=02+(-2)2r2cos2胃+sin2胃=4r2=4r=2

03

Step 3. Finding the polar coordinates 

We know that,

tan胃=yx, so胃=tan-1yx,-蟺2<胃<蟺2

Putting values, we get

role="math" localid="1646730385944" 胃=tan-1-20胃=tan-1-鈭�胃=-蟺2

So, the polar coordinate will be 2,-蟺2.

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