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Chapter 9: Q. 56 (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 first 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+22r2cos2胃+sin2胃=22r2=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

胃=tan-120胃=tan-1鈭�胃=蟺2

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

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Most popular questions from this chapter

In Problems 47鈥�52, find the unit vector in the same direction asv:v=i-jv=i-j

True or False The tests for symmetry in polar coordinates are necessary but not sufficient.

The standard equation of a circle with center at -2,5and radius 3is ______ .

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=2-3cos胃

Identify and graph each polar equation. Verify your graph using a graphing utility.
r=2sin3胃
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