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

# reparametrisation - please check my answer? watch

1. The question asked to reparametrise the curve
r(t)=(2/(1+t^2)-1)i + 2t/(1+t^2)j , t>=0
with respect to the arc length measured from the point (1,0).

I first figured out what value of t I would get from (1,0) by satisfying each entry to the corresponding value, where I found t=0 being the initial value.

Then I differentiated r(t), giving r'(t)=(-(4t/(1+t^2)^2)i + (-(2t^2-2)/(1+t^2)^2)j
To get s(t), I squared the coefficients of i and j, took the square root and then integrated, hence integrating (2/1+t^2) between t and 0.
Thus s=arctan(t) and hence t=tan(s/2)
Substituting this into r(t) and simplifying gave me
r(s)=(2cot^2(s/2))i + (sin(s))j

Can someone please tell me if I have done this correctly?
(I didn't type out all lines of working out and I apologise for the lack of latex..)
2. (Original post by ellemay96)
Substituting this into r(t) and simplifying gave me
r(s)=(2cot^2(s/2))i + (sin(s))j

Can someone please tell me if I have done this correctly?
You made a slip in substituting in at the end, for the i-direction.

PS: You can always plot these to see what they give. Wolfram or whatever software you have.
3. (Original post by ghostwalker)
You made a slip in substituting in at the end, for the i-direction.

PS: You can always plot these to see what they give. Wolfram or whatever software you have.
Yes, I made a really silly mistake. I now have cos(s) for the i direction. Thank you for checking it.

Turn on thread page Beta
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: January 20, 2015
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## 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