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

    10
    ReputationRep:
    The question I'm stuck on was this.

    Solve the equation 5cos2x - 3sinx = 4 for 0°≤ x ≤ 360°

    I've put the equation into the form of Rcos(x+a) already. The answer I got was correct according to the text book and I've got this.

    √34 cos (x + 30.96) = 4

    I've then rearranged the formula into x + 30.96 = cos-1(4/√34).

    This is the part I am stuck on for questions like this. How do I find the value of x? Apparently there are two answers, but I don't know what to do to find them.

    PLEASE HELP
    Offline

    17
    ReputationRep:
    (Original post by Jacklicy)
    The question I'm stuck on was this.

    Solve the equation 5cos2x - 3sinx = 4 for 0°≤ x ≤ 360°

    I've put the equation into the form of Rcos(x+a) already. The answer I got was correct according to the text book and I've got this.

    √34 cos (x + 30.96) = 4

    I've then rearranged the formula into x + 30.96 = cos-1(4/√34).

    This is the part I am stuck on for questions like this. How do I find the value of x? Apparently there are two answers, but I don't know what to do to find them.

    PLEASE HELP
    So x is just:

    x = cos^-1(4/√34) -30.96

    So work out cos inverse of (4/√34), which would give u the two values
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by 2710)
    So x is just:

    x = cos^-1(4/√34) -30.96

    So work out cos inverse of (4/√34), which would give u the two values
    I've got 15.73 for one of the answers which is correct. How do I find the other one?
    Offline

    1
    ReputationRep:
    (Original post by Jacklicy)
    I've got 15.73 for one of the answers which is correct. How do I find the other one?
    So you managed to pass C1-3 without knowing how to find trig solutions?

    Edit: see my later post.


    Posted from TSR Mobile
    Online

    19
    ReputationRep:
    (Original post by Jacklicy)
    The question I'm stuck on was this.

    Solve the equation 5cos2x - 3sinx = 4 for 0°≤ x ≤ 360°

    I've put the equation into the form of Rcos(x+a) already. The answer I got was correct according to the text book and I've got this.

    √34 cos (x + 30.96) = 4

    I've then rearranged the formula into x + 30.96 = cos-1(4/√34).

    This is the part I am stuck on for questions like this. How do I find the value of x? Apparently there are two answers, but I don't know what to do to find them.

    PLEASE HELP
    5cos2x - 3sinx = 4

    Use cos2x=1-2(sinx)^2

    5(1-2(sinx)^2) -3sinx=4

    5-10(sinx)^2 -3sinx = 4

    -10(sinx)^2 -3sinx +1 = 0

    Therefore sinx=-0.5,0.2

    therefore x=330,210,11.54,168.46
    Offline

    1
    ReputationRep:
    (Original post by Jacklicy)
    The question I'm stuck on was this.

    Solve the equation 5cos2x - 3sinx = 4 for 0°≤ x ≤ 360°

    I've put the equation into the form of Rcos(x+a) already. The answer I got was correct according to the text book and I've got this.

    √34 cos (x + 30.96) = 4

    I've then rearranged the formula into x + 30.96 = cos-1(4/√34).

    This is the part I am stuck on for questions like this. How do I find the value of x? Apparently there are two answers, but I don't know what to do to find them.

    PLEASE HELP
    On further inspection, 5cos2x - 3sinx = 4 cannot be written in Rcos(x + a) form. Take a look at the x's.


    Posted from TSR Mobile
    Offline

    17
    ReputationRep:
    (Original post by Jacklicy)
    I've got 15.73 for one of the answers which is correct. How do I find the other one?
    Look at the cos graph. You have cos^-1(4/√34) = roughly 47 degrees.

    So which other degree also gives u cos 47? Looking at the graph, you will have 360 - 47

    Do it with the precise figures
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by Joshmeid)
    On further inspection, 5cos2x - 3sinx = 4 cannot be written in Rcos(x + a) form. Take a look at the x's.


    Posted from TSR Mobile
    According to my text book it is correct.
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by 2710)
    Look at the cos graph. You have cos^-1(4/√34) = roughly 47 degrees.

    So which other degree also gives u cos 47? Looking at the graph, you will have 360 - 47

    Do it with the precise figures
    Using the correct figures I ended with with 313.3. However my MEI text book reveals the second answer to be 282.4, which is pretty confusing.
    Offline

    17
    ReputationRep:
    (Original post by Jacklicy)
    Using the correct figures I ended with with 313.3. However my MEI text book reveals the second answer to be 282.4, which is pretty confusing.
    Thats correct, but then u need to minus the 30.96, which gives you your answer
 
 
 
  • 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
    Brexit voters: Do you stand by your vote?
    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

    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.