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Chapter 9: Q 26. (page 730)

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

0,-3

Short Answer

Expert verified

The polar coordinates are -3,-蟺2+2办蟺and3,蟺2+2办蟺, for any integer k.

Step by step solution

01

Step 1. Given information.

The given rectangular coordinate is:

0,-3

Herex=0andy=-3

02

Step 2. Find the value of r.

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

r=x2+y2r=02+-32r=0+9r=卤3

03

Step 3. Find the value of θ.

Use the formula tan胃=yx,

tan胃=yx胃=tan-1yx胃=tan-1-30胃=tan-1鈭�

role="math" localid="1649230458419" 胃=-蟺2,蟺2,3蟺2sincetan蟺2=鈭�;tan3蟺2=鈭�

04

Step 4. Find the polar coordinates.

Take r=-3,胃=-蟺2,thenr,胃=-3,-蟺2,

The coordinates of r,胃are-3,-蟺2+2办蟺for any integer k.


Now take r=3,胃=蟺2,thenr,胃=3,蟺2,

The coordinates of r,胃are3,蟺2+2办蟺, for any integer k.


Therefore, all the polar coordinates are -3,-蟺2+2办蟺and3,蟺2+2办蟺,

for any integer k.

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Most popular questions from this chapter

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤5,1), major axis6
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