Turn on thread page Beta
    • Thread Starter
    Offline

    13
    ReputationRep:
    a) 5sinx-20sin^3x+16sin^5x

    b) 5sinx-20sin^3x+14sin^5x

    c) 5sinx-10sin^2x+10sin^3x-5sin^4x+sin^5x

    d) sinx-5sin^2x+10sin^3x-10sin^4x+5sin^5x


    The answer is a) but the question is on an old Oxford exam.... Most of the questions for the same number of marks didn't take anywhere near as long to work out, the method I used for this was quite laborious... Is there an easier way?
    Offline

    10
    ReputationRep:
    Complex numbers.
    • Thread Starter
    Offline

    13
    ReputationRep:
    how?
    Offline

    15
    ReputationRep:
    (Original post by sebbie)
    a) 5sinx-20sin^3x+16sin^5x

    b) 5sinx-20sin^3x+14sin^5x

    c) 5sinx-10sin^2x+10sin^3x-5sin^4x+sin^5x

    d) sinx-5sin^2x+10sin^3x-10sin^4x+5sin^5x


    The answer is a) but the question is on an old Oxford exam.... Most of the questions for the same number of marks didn't take anywhere near as long to work out, the method I used for this was quite laborious... Is there an easier way?
    it's fairly easy to work out which is correct by a process of elimination

    (c) and (d) aren't odd but the given function is

    (b) disagrees with the given function at pi/2 giving 5-20+14 = -1 rather than 1
    Offline

    10
    ReputationRep:
    (Original post by RichE)
    it's fairly easy to work out which is correct by a process of elimination

    (c) and (d) aren't odd but the given function is

    (b) disagrees with the given function at pi/2 giving 5-20+14 = -1 rather than 1
    Aaah, that's much more clever.
    Offline

    2
    ReputationRep:
    (Original post by sebbie)
    how?
    You may know that \sin(nx) = \frac{(cos x + isin x)^n - (cos x - i sin x)^n}{2i}. Use the binomial expansion on this and mess around a bit, you should end up with \sin nx = \sum_k^n nCk sin (\frac{n-k}{2}\pi) cos^k x sin^{n-k} x. You can rewrite the even powers of cos in terms of sine using the Pythagorean identity (note there will only be even powers of sine in the expansion of an odd n, you should see why from the first sine term in the last formula I wrote). You can evaluate this expression for n=5.

    Anyway, RichE's method is of course a much better approach (and the kind of approach I wouldn't think of )

    In other news, I officially despise mimetex :mad:
    Offline

    13
    ReputationRep:
    \huge
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 10, 2006

University open days

  • Heriot-Watt University
    School of Textiles and Design Undergraduate
    Fri, 16 Nov '18
  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
Poll
Have you ever experienced bullying?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.