Login

Search the forums now!

Welcome, Guest. Please login or register.

November 01, 2025, 03:13:36 pm
Pages: [1]   Go Down

Author Topic: fun parametric equation  (Read 2524 times)  Share 

0 Members and 1 Guest are viewing this topic.

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
fun parametric equation
« on: April 06, 2010, 09:49:00 pm »
0
I think this is in the domain (no pun intended) of Spech maths, so I will ask it here.

Parametric curves defined by:



Find the cartesian equation.

Ok so this requires slightly more creativity than the normal ones. I recognised that if you square both sides, they will give you a term which will no doubt cancel.

So I did thus, let for simplicity of typing (no, i will not Copy paste thank you very much)



Squaring both sides yields:




Undoubtably, adding the two equations we get:


so

Then cartesian equation is:



Is this valid?

*edit*: Thanks brightsky
« Last Edit: April 06, 2010, 11:09:07 pm by Martoman »
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

m@tty

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4324
  • Respect: +33
  • School: Heatherton Christian College
  • School Grad Year: 2010
Re: fun parametric equation
« Reply #1 on: April 06, 2010, 09:59:57 pm »
0
It appears so. Why shouldn't it be?
Logged
2009/2010: Mathematical Methods(non-CAS) ; Business Management | English ; Literature - Physics ; Chemistry - Specialist Mathematics ; MUEP Maths

96.85

2011-2015: Bachelor of Aerospace Engineering and Bachelor of Science, Monash University

2015-____: To infinity and beyond.

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: fun parametric equation
« Reply #2 on: April 06, 2010, 10:04:27 pm »
0
Specialist book has this insanely contrived answer, this is q12 dii from ext-res chapter 5 btw.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: fun parametric equation
« Reply #3 on: April 06, 2010, 10:24:40 pm »
0
Soz for hi-jacking your thread Martoman...I got a related question...

Show that the rational points on the circle can all be found by the parametrization:



By constructing a line segment of gradient from the known rational point (-1,0).


Do you do this by solving and simultaneously?
« Last Edit: April 06, 2010, 10:28:33 pm by brightsky »
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: fun parametric equation
« Reply #4 on: April 06, 2010, 10:35:34 pm »
0
Quote from: brightsky on April 06, 2010, 10:24:40 pm
Soz for hi-jacking your thread Martoman...I got a related question...

Show that the rational points on the circle can all be found by the parametrization:



By constructing a line segment of gradient from the known rational point (-1,0).


Do you do this by solving and simultaneously?

In short? Yes. Just reject the x=-1, y = 0 fail solution.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

kamil9876

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1943
  • Respect: +109
Re: fun parametric equation
« Reply #5 on: April 06, 2010, 10:39:53 pm »
0
that's a historical classic :) I think Diophantus was the first to do this. Check here.
Logged
Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

/0

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4124
  • Respect: +45
Re: fun parametric equation
« Reply #6 on: April 06, 2010, 10:43:12 pm »
0
That is (also) known as the weierstrass substitution

It is useful for turning integration problems involving sines and cosines into simple rational functions.
Logged

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: fun parametric equation
« Reply #7 on: April 06, 2010, 10:55:21 pm »
0
Quote from: /0 on April 06, 2010, 10:43:12 pm
That is (also) known as the weierstrass substitution

It is useful for turning integration problems involving sines and cosines into simple rational functions.

HOW DO YOU KNOW THIS? ahahaah you are getting karma for it.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

TrueTears

  • TT
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 16363
  • Respect: +667
Re: fun parametric equation
« Reply #8 on: April 06, 2010, 10:58:03 pm »
0
coz /0 is insane at maths thats why
Logged
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: fun parametric equation
« Reply #9 on: April 06, 2010, 11:02:59 pm »
0
Quote from: TrueTears on April 06, 2010, 10:58:03 pm
coz /0 is insane at maths thats why

I always thought maths wasn't much about knowledge, then again, now i can integrate trig functions without thinking!
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: fun parametric equation
« Reply #10 on: April 06, 2010, 11:06:45 pm »
0
Quote from: Martoman on April 06, 2010, 09:49:00 pm
I think this is in the domain (no pun intended) of Spech maths, so I will ask it here.

Parametric curves defined by:



Find the cartesian equation.

Ok so this requires slightly more creativity than the normal ones. I recognised that if you square both sides, they will give you a term which will no doubt cancel.

So I did thus, let for simplicity of typing (no, i will not Copy paste thank you very much)



Squaring both sides yields:




Undoubtably, adding the two equations we get:


so

Then cartesian equation is:



Is this valid?

Is it me or is this supposed to be instead..
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

Martoman

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1476
  • Respect: +11
Re: fun parametric equation
« Reply #11 on: April 06, 2010, 11:08:20 pm »
0
Um yes, switch em.
Logged
2009: Math methods: 50, Psychology: 44
2010: chem 47, further 48, Spesh 49 fml seriously and other yr 11 subs.
2011: Holidaying, screw school.
No. Not azn.
___________________________________
Swedish meal time all the time

/0

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4124
  • Respect: +45
Re: fun parametric equation
« Reply #12 on: April 06, 2010, 11:18:26 pm »
0
Quote from: Martoman on April 06, 2010, 11:02:59 pm
Quote from: TrueTears on April 06, 2010, 10:58:03 pm
coz /0 is insane at maths thats why

I always thought maths wasn't much about knowledge, then again, now i can integrate trig functions without thinking!

lol TT also knew this, he studied from Stewart Calculus like I did
Logged
Pages: [1]   Go Up