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    Okay so the question is simply Solve, for 0<x<360,

    \cos 3x = -\frac{1}{2}

    Now I can work out that 3x=120, so x=40
    ... and then I've done 360+120=480 ... 480/3=160
    ... and finally 720+120=840 ... 840/3=280

    So the three x values I got were 40, 160 and 280. Now I would have left it at that but the mark scheme says there is also 80, 200 and 320. I don't understand where these are coming from, could anyone help me out please?

    (By the way, this is question 9 part B on C2's June 2008 paper.)
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    it's the same as solving cos u = -0.5 for 0<u<1080, then dividing the values of u by 3.
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    0<x<360, so 0<3x<1080.
    Solve cos3x=-0.5 for this with all the values of 3x between 0 and 1080. Divide by 3. Done.
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    There was probably a square root somewhere in the question. In this case you have to take the minus square root as well and do the same thing, the other answers should come out as well.

    Edit : No, i'm wrong. There are more solutions to cos3x than just every 360 degrees
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    Also with this type of question, it's usually a good idea to draw a little graph of the trig function you are working with so you can just read the solutions off that rather than trying to do it algebraically.
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    since its 3x, times the range by 3

    So 0 <x<1080

    cos x = -1/2

    solutions consist of: 3x = 120, 240, 480, 600, 840, 960

    therefore x = 40, 80, 160,200, 280, 320.
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    Like the others said, you just need to adjust it to 0<3x<1080.

    Think it through and understand it before you move on. It'll make your life easier if you can get your head around it instead of just learning the steps.

    Understanding is the key to A-level maths.
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    Could someone tell me how to find the other values in the range, like I know cos^(-1)(-1/2) at 120 degrees, but how to find the other values in the range?
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    Ahhh, I get it now. I think I'll be drawing graph sketches in future instead of using the 'bow-tie' method or whatever you wanna call it. Thanks everyone!
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    (Original post by Arcanen)
    Ahhh, I get it now. I think I'll be drawing graph sketches in future instead of using the 'bow-tie' method or whatever you wanna call it. Thanks everyone!
    When You sketch you see that when cosx=-0.5 then
    3x=120^{o}\pm k\cdot 360^{o}
    or
    3x=240^{o}\pm k\cdot 360^{o}

    So the solution

    x=40 \pm k\cdot 120^{o}
    and
    x=80 \pm k\cdot 120^{o}
 
 
 
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