Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    write down the taylor polynomial of order n=4 generated by the function f(x)=cos^2(x) - sin^2(x) at x=0.

    teacher has written:

    "note that f(x)=cos2x" why has he done cos2x rather than cos^2(x)? and why doesn't he mention the -sin^2(x)?

    "then P4(x)= 1 - 2x^2 + (2/3)x^4" he's given no steps whatsoever and i've no idea how he's done it. also, the P4, the "4" is small, i've no idea what this stands for either!

    :lolwut:

    can anyone help?? thank you
    Offline

    12
    ReputationRep:
    Try using some double angle formulae for cos to see how your teacher transformed it into cos(2x)...
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by furryvision)
    "note that f(x)=cos2x" why has he done cos2x rather than cos^2(x)? and why doesn't he mention the -sin^2(x)?
    :dry:

    C3 trig identities: \cos 2x = \cos^2 x - \sin^2 x.

    (Original post by furryvision)
    "then P4(x)= 1 - 2x^2 + (2/3)x^4" he's given no steps whatsoever and i've no idea how he's done it. also, the P4, the "4" is small, i've no idea what this stands for either!
    I assume Pn is meant to stand for "the first few terms of the Taylor expansion up to the term in x^n".

    You're trying to expand cos 2x. If you know the Taylor expansion for cos u, then just write it out and put u = 2x, and it should come out. If you don't, you should start differentiating cos 2x and work from the definition of Taylor series.
 
 
 
Poll
Who is your favourite TV detective?
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.