x Turn on thread page Beta
 You are Here: Home >< Maths

# FP2 Polar equations watch

1. 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???
2. (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.
3. (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??
4. (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).
5. (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.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 19, 2015
Today on TSR

### Negatives of studying at Oxbridge

What are the downsides?

### Grade 9 in GCSE English - AMA

Poll
Useful resources

Can you help? Study help unanswered threadsStudy Help rules and posting guidelinesLaTex guide for writing equations on TSR

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE