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Chapter 9: Q. 64 (page 568)

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

-0.8,-2.1

Short Answer

Expert verified

The polar coordinates is 5.05,4.34.

Step by step solution

01

Step 1. Given Information

We are given rectangular coordinates of a point,

-0.8,-2.1

We have to find polar coordinates of given point.

02

Step 2. Finding the polar coordinates    

The distance of the point -0.8,-2.1from origin is given by,

r=x2+y2r=(-0.8)2+-2.12=0.64+4.41=5.05

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

localid="1646797452204" 胃=tan-1-2.1-0.8=tan-1(2.625)=-1.2

Since, the point is in the third quadrant, so by adding 蟺=3.14, we get the angle in third quadrant.

胃=3.14+1.2胃=4.34

So, the polar coordinate will be role="math" localid="1646797577326" 5.05,4.34.

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