Turn on thread page Beta
    • Thread Starter
    Offline

    7
    ReputationRep:
    I thought I'd make this thread, since one always gets made for each maths exam. You can post questions, feedback from the exam tomorrow, and most importantly of all, play with the maths symbols!

    remember: (∂s)² = (∂x)² + (∂y)²

    therefore: (∂s/∂x)² = 1 + (∂y/∂x)²

    which implies that s = ∫√[1 + (dy/dx)²]dx

    I love the maths symbols
    Offline

    15
    ReputationRep:
    (Original post by inequality)
    I thought I'd make this thread, since one always gets made for each maths exam. You can post questions, feedback from the exam tomorrow, and most importantly of all, play with the maths symbols!

    remember: (∂s)² = (∂x)² + (∂y)²

    therefore: (∂s/∂x)² = 1 + (∂y/∂x)²

    which implies that s = ∫√[1 + (dy/dx)²]dx

    I love the maths symbols
    Probably best not to write partial derivative for the above - doesn't really make sense in the first equation and is technically true in the second but is unnecessary
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by RichE)
    Probably best not to write partial derivative for the above - doesn't really make sense in the first equation and is technically true in the second but is unnecessary
    Well it does. I don't know about partial derivatives, but the top one it just pythagoras theorem for small increses in x and y. Anyway, I like the little deltas
    Offline

    15
    ReputationRep:
    (Original post by inequality)
    Well it does. I don't know about partial derivatives, but the top one it just pythagoras theorem for small increses in x and y. Anyway, I like the little deltas
    Yes but  \delta x and  \partial x mean different things and you should use the former if that's what you meant
    Offline

    2
    ReputationRep:
    is arcsec the same as 1/arcos?
    Offline

    12
    ReputationRep:
    (Original post by lgs98jonee)
    is arcsec the same as 1/arcos?
    arcsecx = arccos(1/x)
    Offline

    0
    ReputationRep:
    hi

    I can't find any help in the book for deriving cartesian equations from intrinsic equations!?!?!?

    Can anyone find a cartesian equation for

    s = 12sin2ω (where s is measured from O)

    show that it's (8 - x)(2/3) + y(2/3) = 4

    Thanks in advance
    Offline

    15
    ReputationRep:
    For a summary of intrinsics and other P5 related matters see this thread http://www.thestudentroom.co.uk/t116149.html
    Offline

    1
    ReputationRep:
    What's an intrinsic equation? They aren't in P5 are they?
    Offline

    15
    ReputationRep:
    find a cartesian equation for
    s = 12sin2ω (where s is measured from O)
    show that it's (8 - x)(2/3) + y(2/3) = 4
    s=12sin^{2}\psi \\

\frac{ds}{d\psi }=24sin\psi cos\psi\\

ds=24sin\psi cos\psi d\psi\\

\frac{dy}{ds}=sin\psi\\

y=\int sin\psi ds\\

y=\int (sin\psi)(24sin\psi cos\psi) d\psi\\

y=\int (24sin^{2}\psi cos\psi) d\psi\\

y=\frac{24}{3}sin^{3}\psi + C\\

y=\8sin^{3}\psi as x=y=w=s=0 at O.
    \frac{dx}{ds}=cos\psi\\

x=\int 24sin\psi cos^{2}\psi\\

x=-8cos^{3}\psi + C\\

x=-8cos^{3}\psi+8\\

(8-x)^{\frac{2}{3}}+y^{\frac{2}{3}}  \\

=(8cos^{3}\psi)^{\frac{2}{3}}+(8  sin^{3}\psi) ^{\frac{2}{3}}\\

=4
    Offline

    2
    ReputationRep:
    (Original post by Showsni)
    What's an intrinsic equation? They aren't in P5 are they?
    Edexcel P5, yeah.
    They're in the Coordinate Systems topic (last chapter).
    Offline

    0
    ReputationRep:
    (Original post by Gaz031)
    For a summary of intrinsics and other P5 related matters see this thread http://www.thestudentroom.co.uk/t116149.html
    Cheers guv, got it from that
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by RichE)
    Yes but  \delta x and  \partial x mean different things and you should use the former if that's what you meant
    Ahh yes sorry. Where do I get little delta then?
    Offline

    0
    ReputationRep:
    (Original post by Gaz031)
    s=12sin^{2}\psi \\

\frac{ds}{d\psi }=24sin\psi cos\psi\\

ds=24sin\psi cos\psi d\psi\\

\frac{dy}{ds}=sin\psi\\

y=\int sin\psi ds\\

y=\int (sin\psi)(24sin\psi cos\psi) d\psi\\

y=\int (24sin^{2}\psi cos\psi) d\psi\\

y=\frac{24}{3}sin^{3}\psi + C\\

y=\8sin^{3}\psi as x=y=w=s=0 at O.
    \frac{dx}{ds}=cos\psi\\

x=\int 24sin\psi cos^{2}\psi\\

<b>x=-8cos^{3}\psi + C\\</b>

x=-8cos^{3}\psi\\

(8-x)^{\frac{2}{3}}+y^{\frac{2}{3}}  \\

=(8+8cos^{3}\psi)^{\frac{2}{3}}+  (8sin^{3}\psi)^{\frac{2}{3}}
    I think you left out the +8 on the x term
    Offline

    1
    ReputationRep:
    Edexcel P5, yeah.
    They're in the Coordinate Systems topic (last chapter).
    That's a relief - I'm doing OCR P5 tomorrow.
    Offline

    15
    ReputationRep:
    (Original post by Master Gee)
    I think you left out the +8 on the x term
    Thanks.
    I was working through it while texing and found it difficult to read so I posted it so that I could read what i had :rolleyes:
    Offline

    2
    ReputationRep:
    (Original post by BCHL85)
    arcsecx = arccos(1/x)

    are you sure?
    Offline

    12
    ReputationRep:
    (Original post by lgs98jonee)
    are you sure?
    Let y = arcsecx -> x = secy = 1/cosy
    -> cosy = 1/x
    -> y = arccos(1/x)
    Offline

    0
    ReputationRep:
    Does anyone know what even and odd function are?

    e.g. show that coshx is an even function
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by Master Gee)
    Does anyone know what even and odd function are?

    e.g. show that coshx is an even function
    Even functions are symmetric about the y axis, or to put it another way:

    f(x) = f(-x)

    cosh(x) = cosh(-x) [think in terms of e]

    therefore it's even.
 
 
 
Turn on thread page Beta
Updated: June 19, 2005
The home of Results and Clearing

3,045

people online now

1,567,000

students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
Poll
A-level students - how do you feel about your results?
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.