Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    Hi,
    I am going to attatch some workings I have done for a Trig Question. Bearing in mind I have taught myself this topic today so I am a bit rusty. I will also attach the mark scheme so please could someone please explain where I have gone wrong? Thank you so much.

    Amelia
    Attachment 695792Attachment 695798
    Attached Images
        
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by aliasanoynmous)
    Hi,
    I am going to attatch some workings I have done for a Trig Question. Bearing in mind I have taught myself this topic today so I am a bit rusty. I will also attach the mark scheme so please could someone please explain where I have gone wrong? Thank you so much.

    Amelia
    Attachment 695792Attachment 695798
    I think it's mostly okay after a quick read through. But can you explain how you got the \frac{7}{12}\pi solution?

    Of course you're not using "hence" in this case so your working won't follow the mark scheme but that's fine. The "hence" method is quicker but can be confusing for a lot of students.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Notnek)
    I think it's mostly okay after a quick read through. But can you explain how you got the \frac{7}{12}\pi solution?

    Of course you're not using "hence" in this case so your working won't follow the mark scheme but that's fine. The "hence" method is quicker but can be confusing for a lot of students.
    Thank you for checking my anwer.I got this answer because when using the cast diagram I was under the impression that if you were doing the inverse of a negative number you had to make it positive when finding your answer. Then, instead of using the "tan" and "all" regions of the diagram you use the "sin" and "cos" regions. Thus, what I have done here. This has usually worked with the other questions and in L6.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by aliasanoynmous)
    Thank you for checking my anwer.I got this answer because when using the cast diagram I was under the impression that if you were doing the inverse of a negative number you had to make it positive when finding your answer. Then, instead of using the "tan" and "all" regions of the diagram you use the "sin" and "cos" regions. Thus, what I have done here. This has usually worked with the other questions and in L6.
    Where did the \frac{7}{12}\pi solution come from : the = 2 + \sqrt{3} equation or the = -2 + \sqrt{3} equation?

    I can't see the -\frac{1}{12}\pi solution on any CAST diagram so I'm wondering if you've considered it?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Notnek)
    Where did the \frac{7}{12}\pi solution come from : the = 2 + \sqrt{3} equation or the = -2 + \sqrt{3} equation?

    I can't see the -\frac{1}{12}\pi solution on any CAST diagram so I'm wondering if you've considered it?
    The CAST diagram is on my second page of workings. No I did not include the (-1)/12 on any CAST diagram because it is negative. The 7/12pi came from the -2+root3. So I did tan^-1 of 2+root3 which gave 5/12pi then I did pi- 5/12pie to get 7/12pi.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by aliasanoynmous)
    The CAST diagram is on my second page of workings. No I did not include the (-1)/12 on any CAST diagram because it is negative. The 7/12pi came from the -2+root3. So I did tan^-1 of 2+root3 which gave 5/12pi then I did pi- 5/12pie to get 7/12pi.
    It seems like you might be missing some understanding of the CAST diagram.

    You should have two separate CAST diagrams for the two equations and you shouldn't be mixing up the two which you have done I think.

    So for \tan \theta = 2 + \sqrt{3}, you use your calculator to get the solution \theta = \frac{5\pi}{12} which you did. Then 2+\sqrt{3} is positive so you're looking for solutions in A and T. The T solution goes beyond the range and you already have the A solution so you're done for this equation i.e. the only solution is \frac{5\pi}{12}. Just because the other equation has a negative right-hand-side, this does not affect the first set of solutions.

    Then for \tan \theta = -2 + \sqrt{3}, you need another CAST diagram and first mark on \theta = -\frac{\pi}{12} because this is the calculator solution. Then since -2+\sqrt{3} is negative, you need to find soltutions in the S quadrant, since this is the only negative quadrant in the range.

    If you're still stuck, please explain which specific part of my post you didn't understand. Explaining/understanding CAST in a forum post can be hard

    Also it's very important that you understand what you're doing when using the CAST diagram and not just copying a method. If you feel you don't understand it fully then I recommend watching videos on the topic.
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by aliasanoynmous)
    The CAST diagram is on my second page of workings. No I did not include the (-1)/12 on any CAST diagram because it is negative. The 7/12pi came from the -2+root3. So I did tan^-1 of 2+root3 which gave 5/12pi then I did pi- 5/12pie to get 7/12pi.
    More importantly, have you looked at the mark scheme method to understand what they did?

    When you see the word "Hence" in a maths question it's usually a pointer to tell you that you can get a particular result fairly efficiently by using previous parts of a question. In this case you've made yourself an awful lot of extra work - and introduced the possibility of errors - by attacking the problem in a roundabout manner
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 15, 2017

University open days

  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
  • Bournemouth University
    Undergraduate Open Day Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
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.