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

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

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)*

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

In polar coordinates r is always positive.

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

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

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

.

Great to hear from you again!!!

Bob

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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

Hi Bob!

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

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!

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

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!

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

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

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!

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