The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

FP2 Polar equations

So I am required to write the Cartesian equation
(x-1)^2 + (y-1)^2 = 2 into polar form.

I did this easily by simple substitution of the results x=rcosΘ and y=rsinΘ to obtain the correct solution of r=2(cosΘ+sinΘ) however the answer also requires

-(1/4)pi <Θ<(3/4)pi to be stated. I don't understand how to work out these ranges of validity for these equations at all so how do I get to this???
Original post by Mathematicus65
So I am required to write the Cartesian equation
(x-1)^2 + (y-1)^2 = 2 into polar form.

I did this easily by simple substitution of the results x=rcosΘ and y=rsinΘ to obtain the correct solution of r=2(cosΘ+sinΘ) however the answer also requires

-(1/4)pi <Θ<(3/4)pi to be stated. I don't understand how to work out these ranges of validity for these equations at all so how do I get to this???


You can see from the Cartesian equation that the circle goes through the origin. You need to find the values of theta for which this happens. Do this by putting r = 0 to get an equation for theta.
Original post by tiny hobbit
You can see from the Cartesian equation that the circle goes through the origin. You need to find the values of theta for which this happens. Do this by putting r = 0 to get an equation for theta.


Okay doing that tells me that cosΘ+sinΘ=0.
Therefore 1=-tanΘ ---> tan^-1(-1)=Θ. Therefore Θ can equal -1/4 pi or 3/4 pi. How do I know the interval is between that range ie -1/4 pi <Θ<3/4 pi
And not outside of it instead??
Original post by Mathematicus65
Okay doing that tells me that cosΘ+sinΘ=0.
Therefore 1=-tanΘ ---> tan^-1(-1)=Θ. Therefore Θ can equal -1/4 pi or 3/4 pi. How do I know the interval is between that range ie -1/4 pi <Θ<3/4 pi
And not outside of it instead??


Look at the sketch you drew from the Cartesian equation (or the one you are about to draw).
Original post by Mathematicus65
Okay doing that tells me that cosΘ+sinΘ=0.
Therefore 1=-tanΘ ---> tan^-1(-1)=Θ. Therefore Θ can equal -1/4 pi or 3/4 pi. How do I know the interval is between that range ie -1/4 pi <Θ<3/4 pi
And not outside of it instead??


Posting the same query in two different threads causes confusion.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you