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Convert the polar equation into rectangular coordinates

  • Thread starter louie3006
  • Start date
  • #1
54
0

Homework Statement


r^2= 2cos^2 θ+3sin^2θ



Homework Equations



X= r cosθ
y= r sinθ

The Attempt at a Solution


√r=√2cos^2 θ+3sin^2θ
r = 2 cos θ+ 3 sin θ
r = 2x + 2 y.
I doubt that i even got close to the correct answer so I like to ask anyone who knows how to deal with this type of equation, Did I make the right moves ( steps ) or did messed it all up ?and if i did, will you please help ( guide ) me to the right way to correct way of doing these type of equations. thanks in advance.

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
33,085
4,792
[tex]\sqrt{a^2 + b^2} \neq a + b[/tex]
√r=√2cos^2 θ+3sin^2θ
r = 2 cos θ+ 3 sin θ
r = 2x + 2 y
I see what you did in your first equation, but the second one doesn't follow from the first, for the reason I gave above. The third doesn't follow from the second.

The relationship is x = rcos θ and y = rsin θ. How did you go from the second equation to the third?

Rather than take square root of both sides, start making replacements using the polar equivalents for x and y. Also, there is a useful formula involving x, y, and r.
 
  • #3
54
0
i know that r =X^2+ Y^2
and what i basically did in the 3rd equation was that i plugged in x instead of Cos θ and Y for Sin θ.
 
  • #4
gabbagabbahey
Homework Helper
Gold Member
5,002
6
i know that r =X^2+ Y^2
and what i basically did in the 3rd equation was that i plugged in x instead of Cos θ and Y for Sin θ.
But x isn't Cos θ : it's r*Cos θ or, in terms of x and y [tex]\sqrt{x^2+y^2}\cos \theta[/tex] and so [tex] \cos \theta=\frac{x}{\sqrt{x^2+y^2}}[/tex] ...how about Sin θ?
 
  • #5
33,085
4,792
i know that r =X^2+ Y^2
Then you know something that isn't true, so isn't really worth knowing.
 
  • #6
Then you know something that isn't true, so isn't really worth knowing.
okay that was kinda harsh! But he's right, you're forgetting something in that r [tex]\neq[/tex] x2+y2 what does r equal? Or maybe, what does r2 equal? :wink:
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,770
911

Homework Statement


r^2= 2cos^2 θ+3sin^2θ
Multiplying on both sides by [itex]r^2[/itex] gives [itex]r^4= 2r^2cos^2 \theta+ 3r^2 sin^2 \theta[/itex] or [itex](r^2)^2= 2(r cos \theta)^2+ 3(r sin \theta)^2[/itex].

Homework Equations



X= r cosθ
y= r sinθ

The Attempt at a Solution


√r=√2cos^2 θ+3sin^2θ
r = 2 cos θ+ 3 sin θ
r = 2x + 2 y.
I doubt that i even got close to the correct answer so I like to ask anyone who knows how to deal with this type of equation, Did I make the right moves ( steps ) or did messed it all up ?and if i did, will you please help ( guide ) me to the right way to correct way of doing these type of equations. thanks in advance.

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

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