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Definitive list of proofs for HL Maths PII

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Comments

  • #32
    Prowetod
    Registered Users, Registered Users 2 Posts: 521 ✭✭✭Prowetod


    The order I will do the questions will most likely be: 8,1,4,5,6,2,3.

    Does anyone know if the line transformation proofs come up in Q3 often?


  • #33
    awhir
    Registered Users, Registered Users 2 Posts: 4,227 ✭✭✭awhir


    doorknob_opener wrote: »
    I tried making it look ''mathsy'', you know with fractions ect..., but the usual mathods I use on a different forum didn't work :(. Since I can't make powers, ^2 means to the powers of 2. And to make it clear, all angles are in brackets.

    1. cos^2(A) + sin^(2) = 1

    2. Cosine formula a^2 = b^2 + c^2 - 2bc cos(A)

    3. cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

    4. cos(2A) = cos^2(A) - sin^2(A)

    5. sin(A+B) = sin(A)cos(B) + cos(A)sin(B)

    6. sin(2A) = 2sin(A)cos(A)

    This is where this might get hard to understand. By / I mean a fraction

    7. tan(A+B) = [tan(A) + tan (B)]/[1 - tan^2(A)]

    8. tan2A = [2tanA]/[1 - tan^2(A)]

    9. cos2A = [1 - tan^2(A)]/[1 + tan^2(A)]

    10. sin2A = [2tanA]/[1 + tan^2(A)]

    11. cos^2(A) = 1/2[1 + cos(2A)]

    12. sin^2(A) = 1/2[1 - cos(2A)]

    If I typed anything wrong let me know. Good luck deciphering :D


    do you have to learn all these or could u just prove them using common sence ?

    gota study all of Q8,Q4,Q5 in 3hours its gona be tough ! :o


  • #34
    Killaqueen!!!
    Closed Accounts Posts: 2,026 ✭✭✭Killaqueen!!!


    Des23 wrote: »
    Has the difference equation proof ever come up?
    Could definitely see it happening, people usually take it as a straightforward 20 marks, if they are out to mix things up a bit...

    2007

    It's an annoying enough proof...what it is your actually proving? I know how to do it but I dunno what it is I am doing! It ends up equal to zero or something..


  • #35
    sock puppet
    Registered Users, Registered Users 2 Posts: 4,586 ✭✭✭sock puppet


    Not really sure how I'm going to go in this paper. I always go way over time on the circle question. I'll probably make it up on probability though.

    And can someone help me with the proof of sin(a+b)? My book says to use the formula for cos(a-b) and substitute (pi/2 - a) in for a. Does cos(pi/2-a) = sin a?


  • #36
    platypus
    Registered Users, Registered Users 2 Posts: 372 ✭✭platypus


    sock puppet wrote: »
    Not really sure how I'm going to go in this paper. I always go way over time on the circle question. I'll probably make it up on probability though.

    And can someone help me with the proof of sin(a+b)? My book says to use the formula for cos(a-b) and substitute (pi/2 - a) in for a. Does cos(pi/2-a) = sin a?


    Yes for this proof you need to remember cos(90-A)=sinA and sin(90-A)=cosA


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  • #37
    [Deleted User]
    Posts: 4,630 ✭✭✭ [Deleted User]


    sock puppet wrote: »
    Not really sure how I'm going to go in this paper. I always go way over time on the circle question. I'll probably make it up on probability though.

    And can someone help me with the proof of sin(a+b)? My book says to use the formula for cos(a-b) and substitute (pi/2 - a) in for a. Does cos(pi/2-a) = sin a?

    Sin(90-A) is equal to cos(A), likewise, cos(90-A) = sin(A). It makes sense if you do a few examples on your calculator. For example:

    Sin(90-30) = cos(30); sin(60) = cos(30). It's basically because, simply, cosine and sine are two sides of the one coin.


  • #38
    ya-ba-da-ba-doo
    Closed Accounts Posts: 884 ✭✭✭ya-ba-da-ba-doo


    ^ yeah cos(pi/2-A)=sinA and sin(pi/2-A)=cosA


  • #39
    xOxSinéadxOx
    Registered Users, Registered Users 2 Posts: 2,604 ✭✭✭xOxSinéadxOx


    awhir wrote: »
    do you have to learn all these or could u just prove them using common sence ?

    gota study all of Q8,Q4,Q5 in 3hours its gona be tough ! :o


    no you don't have to learn them. they're just the trig identities
    the proofs are
    Circle:
    Tangent Theorem

    Line:
    Angle between 2 lines
    Perpindicular Distacen

    Trig:
    Cos^2A + Sin^2A = 1
    compund angle formulae
    cosine rule

    Discrete Maths:
    difference euqation theorem

    trying to learn these all now :o:(

    spent all day yesterday studying maths and I'm still screwed. I've done no irish either
    aarrrgh


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