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    (Original post by SaraBZ)
    Thank you!!!!
    Glad it helped.
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    I have a question.
     f(x)=\sin x , where  x is measured in degrees.
    (a) Sketch the following curves:
    (i)  y=f(x/2), (0\leq x\leq 180) ;
    (i)  y=f(2x), (0 \leq x \leq 450) ;
    (i)  y=f(x+90) , (0\leq x \leq 360) .
    (b) Hence find a single geometrical transformation that maps the curve of  y=f(x) onto the curve  y=\cos x .
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    (Original post by Ano123)
    I have a question.
     f(x)=\sin x , where  x is measured in degrees.
    (a) Sketch the following curves:
    (i)  y=f(x/2), (0\leq x\leq 180) ;
    (i)  y=f(2x), (0 \leq x \leq 450) ;
    (i)  y=f(x+90) , (0\leq x \leq 360) .
    (b) Hence find a single geometrical transformation that maps the curve of  y=f(x) onto the curve  y=\cos x .
    For the first one I believe you would have to stretch the graph by a scale factor of two, in other words multiply the x coordinates by 2 and plot them.

    2. You would have to do the opposite so divide the x coordinates by 2 and plot them.

    3. You are going to have to shift the graph 90 degrees to the left, so just move every point 90 degrees backwards.

    For the last one I need to have a look at the diagram, as they can differ.

    Hope that helps.
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    (Original post by hamza772000)
    For the first one I believe you would have to stretch the graph by a scale factor of two, in other words multiply the x coordinates by 2 and plot them.

    2. You would have to do the opposite so divide the x coordinates by 2 and plot them.

    3. You are going to have to shift the graph 90 degrees to the left, so just move every point 90 degrees backwards.

    For the last one I need to have a look at the diagram, as they can differ.

    Hope that helps.
    Would you be able to sketch them and see if you can do part b.
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    (Original post by Ano123)
    Would you be able to sketch them and see if you can do part b.
    maybe, if you could tell me what paper they're in.
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    (Original post by hamza772000)
    maybe, if you could tell me what paper they're in.
    Iv'e got sketches of the curves using a graphing calculator, so you can try part b.
    Name:  qwertyuio.png
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    (Original post by Ano123)
    Iv'e got sketches of the curves using a graphing calculator, so you can try part b.
    Name:  qwertyuio.png
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Size:  48.9 KB
    Right, so if you were talking about mapping the red graph on to the blue one, I'd say y=f(x+90), because they both seem to be the same height and width, the only difference is that the red one seems to be 90 degrees ahead of the blue one.

    If you look at the point where the y coordinates for both graphs=-1, then you would see that the x coordinates for the blue one=180 degrees and x coordinates for the red one= 270 degrees. 270-180=90, therefore they are 90 degrees apart and the red one is 90 degrees ahead.

    Hope that makes sense.
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    (Original post by hamza772000)
    Right, so if you were talking about mapping the red graph on to the blue one, I'd say y=f(x+90), because they both seem to be the same height and width, the only difference is that the red one seems to be 90 degrees ahead of the blue one.

    If you look at the point where the y coordinates for both graphs=-1, then you would see that the x coordinates for the blue one=180 degrees and x coordinates for the red one= 270 degrees. 270-180=90, therefore they are 90 degrees apart and the red one is 90 degrees ahead.

    Hope that makes sense.
    You seem to be a very bright mathematician. Aiming for A* i presume? Taking maths/FM A-level?
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    Can anyone tackle this?
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    (Original post by Ano123)
    You seem to be a very bright mathematician. Aiming for A* i presume? Taking maths/FM A-level?
    Thanks, and yes I am taking Maths and FM, but I have a question. Did you post that question because you needed help or was that just a question you posted for people to try out? Just curious and a bit confused.
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    (Original post by Ano123)
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    Can anyone tackle this?
    Is it 46 degrees?
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    (Original post by hamza772000)
    Thanks, and yes I am taking Maths and FM, but I have a question. Did you post that question because you needed help or was that just a question you posted for people to try out? Just curious and a bit confused.
    I post questions for people to try out. And yes it is 46 degrees.
    What do you plan on doing after sixth form/college?
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    (Original post by Ano123)
    I post questions for people to try out. And yes it is 46 degrees.
    What do you plan on doing after sixth form/college?
    Ahh. I would love to get a degree in Engineering. Thanks a lot for the questions.
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    (Original post by hamza772000)
    Ahh. I would love to get a degree in Engineering. Thanks a lot for the questions.
    I wish you well in your exams. I may have to post some questions just for you.
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    (Original post by Ano123)
    I wish you well in your exams. I may have to post some questions just for you.
    Haha, Thank you so much!
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    (Original post by Ano123)
    I wish you well in your exams. I may have to post some questions just for you.
    Any more questions?
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    (Original post by hamza772000)
    Any more questions?
    Prove algebraically that if  k is a posiitive integer greater than 1,  k^3 - k is always divisible by 6. (May be more difficult than normal questions of this type as you won't immediately see that there is a factor of 6 to take out).
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    (Original post by Ano123)
    Prove algebraically that if  k is a posiitive integer greater than 1,  k^3 - k is always divisible by 6. (May be more difficult than normal questions of this type as you won't immediately see that there is a factor of 6 to take out).
    Unfortunately, I couldn't get this one, after a lot of attempts I some how got to k^2+3k+2, which makes no sense, I know. Could you please explain it, would be much appreciated.
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    (Original post by hamza772000)
    Unfortunately, I couldn't get this one, after a lot of attempts I some how got to k^2+3k+2, which makes no sense, I know. Could you please explain it, would be much appreciated.
    If you factorise it you get  (k-1)k(k+1) which is the product of 3 consecutive integers. If you think about it, one of the numbers in 3 consecutive integers is a multiple of 3 and one of them (at least) is a multiple of 2. So you have a multiple of 2 multiplied by a multiple of 3, so product of 3 consecutive Integers is divisible by 6.
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    (Original post by Ano123)
    If you factorise it you get  (k-1)k(k+1) which is the product of 3 consecutive integers. If you think about it, one of the numbers in 3 consecutive integers is a multiple of 3 and one of them (at least) is a multiple of 2. So you have a multiple of 2 multiplied by a multiple of 3, so product of 3 consecutive Integers is divisible by 6.
    WOW, thanks. I understand it now. I never thought of it that way. It makes sense now!
 
 
 
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