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Chapter 9: Q. 13 (page 730)

Find all polar coordinates that represent the point (1,0)given in rectangular coordinates.

Short Answer

Expert verified

The polar coordinates are (-1,(2k+1)蟺),(1,2k蟺), for any integer k

Step by step solution

01

Given information

The rectangular coordinate (1,0).

02

Simplification

Consider the rectangular coordinate (1,0).

The objective is to convert the rectangular coordinates to polar coordinates.

In the coordinate (1,0),x=1and y=0.

To find the value of ruse the equation r=x2+y2.

Then,

r=x2+y2r=(1)2+(0)2[sincex=1,y=0]r=卤1

To calculate 胃use the formula 胃=tan-1yx.

By substituting x,yin the formula,

胃=tan-101[sincex=1,y=0]胃=tan-1(0)胃=蟺,2蟺[sincetan蟺=tan2蟺=0]

Take r=-1,胃=蟺

Then (r,胃)=(-1,蟺)

Thus, 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 (r,胃)are (1,2k蟺),for any integer k.

Therefore, the polar coordinates are (-1,(2k+1)蟺),(1,2k蟺), for any integer k

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Most popular questions from this chapter

Use polar coordinates to graph the conics in Exercises 44鈥�51.

r=21-3cos胃

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixy=-6,focus(2,-8)

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

The limaconr=2+cos胃

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

r=e胃for2k蟺鈮�胃鈮�2(k+1)蟺

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=tan胃
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