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Chapter 9: Q 25. (page 730)

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

1,0

Short Answer

Expert verified

The polar coordinates are -1,2k+1蟺and1,2办蟺, for any integer k.

Step by step solution

01

Step 1. Given information.

The given rectangular coordinate is:

1,0

Herex=1andy=0.

02

Step 2. Find the value of r.

To find the value of r, use the formula r2=x2+y2:

r=x2+y2r=12+02r=1+0r=卤1

03

Step 3. Find the value of θ.

Use the formula tan胃=yx,

胃=tan-1yx胃=tan-101胃=tan-10

胃=蟺,2蟺Since迟补苍蟺=0;tan2蟺=0

04

Step 4. Find the polar coordinates.

Now take r=-1,胃=蟺,

Then r,胃=-1,蟺

The coordinates of r,胃are-1,2k+1蟺 for any integer k.

Now take r=1,胃=2蟺,

Then r,胃=1,2蟺.

The coordinates of localid="1649229808751" r,胃are1,2办蟺, for any integer k.

Therefore, all the polar coordinates are-1,2k+1蟺and1,2办蟺,

for any integer k.

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Most popular questions from this chapter

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