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

P3 Question watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:
    Q1:
    Ok L1 has directional vector -4i+2j+7k
    and L2 has directional vector i-2j-2k

    Calculate the "acute" angle between L1 and L2.

    I managed it using dot product, but ended up with a non-acute angle, yet it requires an acute angle :confused: . Please help.

    Q2:
    Also, integrate: cos3xcosx.dx ---> this shouldnt be a problem I split up cos3x in terms of cos2x and cosx just wanted to check my answer.
    Offline

    0
    ReputationRep:
    For q1, just do 180 - answer to get acute angle. You got an obtuse becuase your lines were not both pointing towards the angle or away from the angle.

    If the questions are hard they will state that the angle is acute. If it is an easy question they will expect you to have the vectors pointing the right way
    Offline

    15
    ReputationRep:
    (Original post by ResidentEvil)
    Q1:
    Ok L1 has directional vector -4i+2j+7k
    and L2 has directional vector i-2j-2k

    Calculate the "acute" angle between L1 and L2.

    I managed it using dot product, but ended up with a non-acute angle, yet it requires an acute angle :confused: . Please help.

    Q2:
    Also, integrate: cos3xcosx.dx ---> this shouldnt be a problem I split up cos3x in terms of cos2x and cosx just wanted to check my answer.
    Acute angle is 180-angle you got

    3x = A + B/2
    6x = a + b

    A-B /2 = x
    2x = a-b
    a=2x+b
    6x = 2x + b + b
    b = 2x
    a = 4x

    Integral of (cos4x + cos2x) / 2
    =1/8sin4x + 1/4sin2x + C
    Offline

    0
    ReputationRep:
    Not sure about part 2, havent got paper but I would do:

    cos3xcosx = cos(2x+x)cosx
    = (cos2xcosx - sin2xsinx)cosx
    = [(cos^2x-sin^2x)cosx - (sin2xcosx - cos2xsinx)]cosx
    = [(2cos^2x - 1)cosx - (2sinxcos^2x - {cos^2x-sin^2x}sinx]cosx
    ...

    is this what you did???
    Offline

    0
    ReputationRep:
    (Original post by imasillynarb)
    Acute angle is 180-angle you got

    3x = A + B/2
    6x = a + b

    A-B /2 = x
    2x = a-b
    a=2x+b
    6x = 2x + b + b
    b = 2x
    a = 4x

    Integral of (cos4x + cos2x) / 2
    =1/8sin4x + 1/4sin2x + C
    What is all this A and B stuff??? where did it come from???

    Is it some of those identities in the formula book
 
 
 
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?

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.