Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
    Offline

    11
    ReputationRep:
    (Original post by Ultimate1)
    I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
    Actually, thats because I think as far as A level is concerned we only consider +ve values of r. If you remove this restriction and let r be -ve as well you'll get 6 loops.

    Edit: After thinking I realised that if r is neg then actually the even ones will have 1/2 as many loops. I think in FP2 you only consider r to be +ve though.
    Offline

    0
    ReputationRep:
    (Original post by anshul95)
    Actually, thats because I think as far as A level is concerned we only consider +ve values of r. If you remove this restriction and let r be -ve as well you'll get 6 loops.
    This is not true. graphing r=sin(3 theta) will give you 3 closed loops, not 6.

    OP, try investigating it for yourself using Wolfram Alpha

    eg http://www.wolframalpha.com/input/?i...n%283+theta%29

    Try it where b is odd or even, then try fractional values of b.
    Try to think about the graph of sin(b*x) and what's going on here.
    Offline

    12
    ReputationRep:
    (Original post by Ultimate1)
    I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
    As far as FP2 is concerned r = sin(2 theta) will only give 2 loops due to the restriction that A2 courses place with respect to r greater than or equal to zero..

    You see 4 loops when you allow the r values to be negative.
    now with r = sin (3 theta) .. one could argue that there are "6 loops" but that the loops obtained from negative r values lie on top of the 3 loops that FP2 syllabi consider to be valid ...
    Offline

    11
    ReputationRep:
    (Original post by StephenNeill)
    This is not true. graphing r=sin(3 theta) will give you 3 closed loops, not 6.

    OP, try investigating it for yourself using Wolfram Alpha

    eg http://www.wolframalpha.com/input/?i...n%283+theta%29

    Try it where b is odd or even, then try fractional values of b.
    Try to think about the graph of sin(b*x) and what's going on here.
    oh....my FP2 book went through drawing r=sin(3theta) and missed out the bits were sin(3theta) were negative. i.e. it only considered 0<theta<pi/3 and
    2pi/3<theta<pi and 4pi/3<theta<5pi/3. The other ranges give -ve r. Can you explain to me what why I am wrong (which looking at Wolfram I clearly am)? Is it because -ve r is intepreted in some way I am not familiar with?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 25, 2011

University open days

  1. University of Cambridge
    Christ's College Undergraduate
    Wed, 26 Sep '18
  2. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  3. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

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

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.