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#1 2017-03-07 18:52:05

davidtrinh
Member
Registered: 2016-12-03
Posts: 10

I can't find the third answer in the polar equations.

I am going to write down a problem below.

(ex) Find the points of intersection of r=1-sin(u) and r=1+sin(u) without drawing their graphs.

This is how I do it.

I equate the two equations and get 1-sin(u)=1+sin(u). Simplifying it gives

sin(u)=0. Solving for u gives 0 and pi. Then, the two points are (1 , pi) and (1 , 0).

They are correct. The answer key gives one more answer (0 , pi/2).

How do you find the third answer without graphing? Thanks for your help.

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#2 2017-03-07 21:23:41

zetafunc
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Registered: 2014-05-21
Posts: 2,213
Website

Re: I can't find the third answer in the polar equations.

The third answer is not a solution. (0, pi/2) does not solve r = 1 + sin(u). Your two answers are correct.

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#3 2017-03-08 08:00:39

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

Re: I can't find the third answer in the polar equations.

Actually, there is another solution, since in polar coordinates the point
is the same one as the point
.

So, another equation that would give you a solution would be

Last edited by anonimnystefy (2017-03-08 08:04:41)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2017-03-08 19:47:02

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: I can't find the third answer in the polar equations.

In polar coordinates r is always positive.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2017-03-09 04:00:28

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

Re: I can't find the third answer in the polar equations.

Except not really.

Here's a link relevant to the original post: Intersection of polar curves


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#6 2017-03-09 04:41:32

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,421

Re: I can't find the third answer in the polar equations.

anonimnystefy wrote:

Actually, there is another solution, since in polar coordinates the point  is the same one as the point

So, another equation that would give you a solution would be

.

up

Great to hear from you again!!!

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  smile

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#7 2017-03-09 05:26:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

Re: I can't find the third answer in the polar equations.

Hi Bob! smile

How've you been?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#8 2017-03-09 06:10:04

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,421

Re: I can't find the third answer in the polar equations.

hi Stefy,

I think my brain is still functioning.

How about you?  Uni beckoning?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  smile

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#9 2017-03-09 12:28:34

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

Re: I can't find the third answer in the polar equations.

Good to know! x)

Yeah, I've been a been lacking in the uni department lately, because I got a temporary job, so I had less time to study, but it's pretty good otherwise! big_smile


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#10 2017-03-09 20:12:53

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,421

Re: I can't find the third answer in the polar equations.

Don't know why I didn't do this earlier:

Mcr7mK6.gif

Clearly three (not two) solutions.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  smile

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