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

    3
    ReputationRep:
    struggling at the moment with proving trig identities and doing the integration parts, does anyone have any advice on how to approach these kinds of questions
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by students1999)
    struggling at the moment with proving trig identities and doing the integration parts, does anyone have any advice on how to approach these kinds of questions
    Remember trig identities. Practice.
    Offline

    2
    ReputationRep:
    (Original post by students1999)
    struggling at the moment with proving trig identities and doing the integration parts, does anyone have any advice on how to approach these kinds of questions
    With the trig identities all you need to do is remember the standard cos^2(x) + sin^2(x) = 1 and then when you want to derive the others you can just divide both sides by sin^2(x) or by cos^2(x). I did this at the start of every C4 paper at the top of my page so that I had them as a reference during the exam
    Also some people in my school found that a helpful way to remember which functions are involved is using the phrases:
    cosy cottage (cosec^2(x) = 1 + cot^2(x))
    sexy tan ( sec^2(x) = 1 + tan^2(x))



    Posted from TSR Mobile
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by stepmaths)
    With the trig identities all you need to do is remember the standard cos^2(x) + sin^2(x) = 1 and then when you want to derive the others you can just divide both sides by sin^2(x) or by cos^2(x). I did this at the start of every C4 paper at the top of my page so that I had them as a reference during the exam
    Also some people in my school found that a helpful way to remember which functions are involved is using the phrases:
    cosy cottage (cosec^2(x) = 1 + cot^2(x))
    sexy tan ( sec^2(x) = 1 + tan^2(x))



    Posted from TSR Mobile
    This is a good method for students who don't know the identities before the exam. But for students targeting the top grades it's really useful for them to know the identities off by heart.

    Sometimes questions won't refer to an identity directly and only students who are very familiar with an identity would recognise what to do. An example: one year there was an exam question which involved the fraction

    \displaystyle \frac{1}{\sin x \cos x}

    Students who knew the \sin 2x identity by heart noticed that the denominator could be written as \frac{1}{2} \sin 2x and so the fraction is equal to 2 \ cosec \ 2x. This change allowed them to progress with the question. Students who weren't as familiar with the identity were much less likely to recognise this.

    Some students become very familiar with the identies after doing loads of practice question. For others, it's a good idea to spend 30 mins one day learning them e.g. look at them then try to write them out and repeat until you can write them without looking. It really doesn't take long to learn them.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by stepmaths)
    With the trig identities all you need to do is remember the standard cos^2(x) + sin^2(x) = 1 and then when you want to derive the others you can just divide both sides by sin^2(x) or by cos^2(x). I did this at the start of every C4 paper at the top of my page so that I had them as a reference during the exam
    Also some people in my school found that a helpful way to remember which functions are involved is using the phrases:
    cosy cottage (cosec^2(x) = 1 + cot^2(x))
    sexy tan ( sec^2(x) = 1 + tan^2(x))



    Posted from TSR Mobile
    thank you for the advice im revising maths now and will give it a go and thanks for the phrases dont think i will be forgetting them anymore hahaha
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by notnek)
    This is a good method for students who don't know the identities before the exam. But for students targeting the top grades it's really useful for them to know the identities off by heart.

    Sometimes questions won't refer to an identity directly and only students who are very familiar with an identity would recognise what to do. An example: one year there was an exam question which involved the fraction

    \displaystyle \frac{1}{\sin x \cos x}

    Students who knew the \sin 2x identity by heart noticed that the denominator could be written as \frac{1}{2} \sin 2x and so the fraction is equal to 2 \ cosec \ 2x. This change allowed them to progress with the question. Students who weren't as familiar with the identity were much less likely to recognise this.

    Some students become very familiar with the identies after doing loads of practice question. For others, it's a good idea to spend 30 mins one day learning them e.g. look at them then try to write them out and repeat until you can write them without looking. It really doesn't take long to learn them.
    thank you for this, dont think i would of got that question either tbh and i definately will be learning the identities off by heart
    Offline

    3
    ReputationRep:
    2[1/2sinxcosx] = 2 . 1/sin2x which when it integrates become 2/sin2x then ln|sin2x| + C where C = 2c.
    Because 2 . 1/2 is the same as saying 1.

    Or if you get 2cosec2x it integrates to -cosec2xcot2x + C which I think may be the correct answer if it is saying about trig identities in the question.
 
 
 
  • 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
    What newspaper do you read/prefer?
    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.