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Chapter 9: Q. 62 (page 568)

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

(-2,-23)

Short Answer

Expert verified

The polar coordinates is 4,4蟺3.

Step by step solution

01

Step 1. Given Information   

We are given rectangular coordinates of a point,

(-2,-23)

We have to find polar coordinates of given point.

02

Step 2. Finding the polar coordinates   

The distance of the point (-2,-23)from origin is given by,

role="math" localid="1646791490159" r=x2+y2r=(-2)2+-232=4+12=16=4

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

胃=tan-1-23-2=tan-1(3)=蟺3

Since the point is on the third quadrant, so we have to add 蟺to get the third quadrant angle,

胃=蟺+蟺3胃=3蟺+蟺3胃=4蟺3

So, the polar coordinate is 4,4蟺3.

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