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

    8
    ReputationRep:
    Hi, I came across this question in an admissions test quite some time ago and didn't get it. Can someone please explain how you could simplify this expression? Thanks!
    \frac{sin^2(x)}{1 + sin^2(x)+sin^4(x)+sin^6(x)...}
    Online

    22
    ReputationRep:
    (Original post by Glavien)
    Hi, I came across this question in an admissions test quite some time ago and didn't get it. Can someone please explain how you could simplify this expression? Thanks!
    \frac{sin^2(x)}{1 + sin^2(x)+sin^4(x)+sin^6(x)...}
    The denominator looks like a geometric series with common ratio sin^2 x, so...?
    Offline

    20
    ReputationRep:
    (Original post by Glavien)
    Hi, I came across this question in an admissions test quite some time ago and didn't get it. Can someone please explain how you could simplify this expression? Thanks!
    \frac{sin^2(x)}{1 + sin^2(x)+sin^4(x)+sin^6(x)...}
    Does the bottom remind you of anything?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Zacken)
    The denominator looks like a geometric series with common ratio sin^2 x, so...?
    Umm, I can't work out the sum of the series as the number of terms is not given. So, could you just work out the sum to infinity?? I am not sure why you would want to do that though.
    Online

    22
    ReputationRep:
    (Original post by Glavien)
    Umm, I can't work out the sum of the series as the number of terms is not given. So, could you just work out the sum to infinity?? I am not sure why you would want to do that though.
    Because there are an infinite number of terms, hence the +\cdots. Had it been +\cdots \sin^n x, then that is n terms. But because it is just 3 dots, it means there are an infinite number of them.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Zacken)
    Because there are an infinite number of terms, hence the +\cdots. Had it been +\cdots \sin^n x, then that is n terms. But because it is just 3 dots, it means there are an infinite number of them.
    So, you work out the sum to infinity them simplify to get (sin^2x)(cos^2x)?
    Online

    22
    ReputationRep:
    (Original post by Glavien)
    So, you work out the sum to infinity them simplify to get (sin^2x)(cos^2x)?
    Yeah, looks right.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Zacken)
    Yeah, looks right.
    Thanks, your help is really appreciated!
    Online

    22
    ReputationRep:
    (Original post by Glavien)
    Thanks, your help is really appreciated!
    No worries. :-)
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.