Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    1) If the two lines y=m(1)x + c(1) and y=m(2) +c(2) intersect and make an acute angle theta, show that

    tan theta = modulus of m(1)m(2)/[1+m(1)m(2)]

    2) Integrate (with limits of pie and 0) (xsinx)^2

    help lol

    i was close on the first- i can get the top but not the bottom.
    Offline

    16
    ReputationRep:
    (Original post by futureaussiecto)
    1) If the two lines y=m(1)x + c(1) and y=m(2) +c(2) intersect and make an acute angle theta, show that

    tan theta = modulus of m(1)m(2)/[1+m(1)m(2)]

    2) Integrate (with limits of pie and 0) (xsinx)^2

    help lol

    i was close on the first- i can get the top but not the bottom.
    For 2)
    x^2.sin^2x

    cos2x = 1-2sin^2x
    => sin^2x = 0.5(1-cos2x)

    => x^2sin^2x = 0.5x^2(1-cos2x) = 0.5x^2 - 0.5x^2cos2x

    Does that help? Do the second bit by parts.
    • Thread Starter
    Offline

    2
    ReputationRep:
    [QUOTE=Widowmaker]
    cos2x = 1-2sin^2x
    => sin^2x = 0.5(1-cos2x)
    [QUOTE]

    if i had remembered that bit i would have got it lol
    Offline

    9
    ReputationRep:
    (Original post by futureaussiecto)
    1) If the two lines y=m(1)x + c(1) and y=m(2) +c(2) intersect and make an acute angle theta, show that

    tan theta = modulus of m(1)m(2)/[1+m(1)m(2)]
    Are you sure that's the answer? Is it not m(1) + m(2) on the top line?

    Anyway, this should help:
    tan(A+B) = tanA + tanB/(1 - tanA.tanB)
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by e-unit)
    Are you sure that's the answer? Is it not m(1) + m(2) on the top line?

    Anyway, this should help:
    tan(A+B) = tanA + tanB/(1 - tanA.tanB)
    actually its m(1)-m(2)

    sowwy
    Offline

    9
    ReputationRep:
    (Original post by futureaussiecto)
    actually its m(1)-m(2)

    sowwy
    Same thing. Do you get it now, though? You just use m1=tanθ1 and m2=tanθ2 and use an identity for tan(θ1-θ2) etc...
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by e-unit)
    Same thing. Do you get it now, though? You just use m1=tanθ1 and m2=tanθ2 and use an identity for tan(θ1-θ2) etc...
    when i first saw it i remembered the addition formulae

    i had

    tan = o/a = m(1)x+C(1)-m(2)x+c(2) divided by m(2)x +c2-[m(1)x + c(1) - m(2)-c(2)] the latter because the intersect is when m1+c1=m2+c2

    ???????
    Offline

    9
    ReputationRep:
    Look at the attached diagram

    Clearly, θ = α - β

    tan(θ) = tan(α - β)
    = (tanα - tanβ)/(1 + tanα.tanβ)

    But, m1 = tanα
    and m2 = tanβ

    So, tan(θ) = (tanα - tanβ)/(1 + tanα.tanβ)
    = (m1 - m2)/(1 + m1m2)
    Offline

    12
    ReputationRep:
    These questions are a joke for admission into the world's best uni for maths at the most prestigious college.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Nima)
    These questions are a joke for admission into the world's best uni for maths at the most prestigious college.
    yeh well ive hardly been doin any maths this year i have been doing physics so my maths is very rusty.

    although i must admit- yes they did seem easy. heres the whole thing

    http://math.mdsalih.com/Data/Oxbridg...iew%20Test.pdf
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 14, 2006
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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.