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

    0
    ReputationRep:
    I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
    Attached Images
     
    Offline

    3
    ReputationRep:
    (Original post by samjohnny)
    I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
    Okay, so let's say I had \sin x = 5 and I had to solve it in the range  0 < x \leq 360 (degrees), I would solve it normally, by using the sine graph or the CAST diagram.

    However, if I had \sin (x+20) = 5 and I had to solve it in the range  0 < x \leq 360 (degrees), because I no longer am dealing with x - instead I'm dealing with x+20 - my range must change. It will now become:

     20 < x+20 \leq 380 (degrees)

    Hence, I have to extend my sine graph (or continue to use the CAST diagram) to find other solutions in that range. Do you get what I'm trying to say? So, what would your range become?

    You also might want to check the two answers you have - I don't quite understand what you've done.
    • Study Helper
    Offline

    7
    ReputationRep:
    (Original post by samjohnny)
    I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
     0\leq\alpha\leq\pi \implies 0\leq5\alpha\leq5\pi \implies 0\leq 5\alpha-\frac{\pi}{4}\leq\frac{19\pi}{4} so we must consider 5\alpha-\frac{\pi}{4}=0,\ \pi,\ 2\pi,\ 3\pi,\ 4\pi giving 5 solutions
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah right, I get it now. Thanks a lot.

    I'm also having a hard time on the one after it. It's attached. Not sure where to start or how to follow through.
    Attached Images
     
    • Study Helper
    Offline

    16
    ReputationRep:
    (Original post by samjohnny)
    Ah right, I get it now. Thanks a lot.

    I'm also having a hard time on the one after it. It's attached. Not sure where to start or how to follow through.
    You want to use the hint they've provided to combine a couple of the cosine terms. Have a play with it and see if you can work out which two can be usefully combined.
    Offline

    3
    ReputationRep:
    (Original post by samjohnny)
    I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
    Firstly
    You should to consider that the sine function is periodic and to solve
    the equation according to this generally

    e.g. 1. When
    \displaystyle \sin \left (5\alpha -\frac{\pi}{4}\right )=0
    then

    \displaystyle 5\alpha -\frac{\pi}{4}=k\cdot 2\pi
    or
    \displaystyle 5\alpha -\frac{\pi}{4}=\frac{3\pi}{4}+k\c  dot 2\pi

    That is
    First solution sequence
    \displaystyle \alpha = \frac{\pi}{20}+k\cdot \frac{2\pi}{5}
    and the second solution sequence
    \displaystyle \alpha = \frac{\pi}{5}+k\cdot \frac{2\pi}{5}

    Secondly.
    From general solutions you have to choose those whiches are in the
    given range for k=0, \pm 1, \pm 2 ...
 
 
 
  • 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.

  • 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.