You are Here: Home >< Maths

# taylor polynomial help! watch

1. 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!

can anyone help?? thank you
2. Try using some double angle formulae for cos to see how your teacher transformed it into cos(2x)...
3. (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)?

C3 trig identities: .

(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.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 5, 2009
The home of Results and Clearing

### 2,343

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Keele University
Sun, 19 Aug '18
2. University of Melbourne
Sun, 19 Aug '18
3. Sheffield Hallam University
Tue, 21 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams