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    I sat the C2 paper in May and achieved a C, and hoping to retake. I've gone over the unofficial markscheme for this year, and the only question I can't wrap my head around is question 9)ii and iii). This is the question below;

    9ii) Given that x=1/5 pi and x=2/5 pi are the 2 smallest +ve solutions of sin(ax)=k where k is a +ve constant, find the values of a and k.

    9iii) Given instead that sin(ax)= root 3 cos (ax), find the two smallest +ve solutions for x giving your answers in exact form in terms of a.

    Any responses would be helpful. Thanks!
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    (Original post by MoniC255)
    I sat the C2 paper in May and achieved a C, and hoping to retake. I've gone over the unofficial markscheme for this year, and the only question I can't wrap my head around is question 9)ii and iii). This is the question below;

    9ii) Given that x=1/5 pi and x=2/5 pi are the 2 smallest +ve solutions of sin(ax)=k where k is a +ve constant, find the values of a and k.

    9iii) Given instead that sin(ax)= root 3 cos (ax), find the two smallest +ve solutions for x giving your answers in exact form in terms of a.

    Any responses would be helpful. Thanks!
    For the first one I'd suggest starting with a sketch of sin(ax) - doesn't matter you can't draw a "proper" scale, but mark the points you're given.

    For the second, rearrange to get a single trig. term. Note that the value comes from one of the standard angles.
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    (Original post by ghostwalker)
    For the first one I'd suggest starting with a sketch of sin(ax) - doesn't matter you can't draw a "proper" scale, but mark the points you're given.

    For the second, rearrange to get a single trig. term. Note that the value comes from one of the standard angles.

    Hi, thanks for the response. I've done that, but haven't got any further.
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    (Original post by MoniC255)
    Hi, thanks for the response. I've done that, but haven't got any further.
    Which part are you refering to and what have you got?
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    (Original post by ghostwalker)
    Which part are you refering to and what have you got?
    To part 9ii. I've drawn a sine graph, and have draw in the given smallest solutions. Do you know what I could do after this please to obtain a and k? Thanks
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    (Original post by MoniC255)
    To part 9ii. I've drawn a sine graph, and have draw in the given smallest solutions. Do you know what I could do after this please to obtain a and k? Thanks
    I was hoping you'd post your diagram, otherwise I'm just going to have to assume it's correct.

    I am assuming that "a" is positive, though your question doesn't state that.

    The standard sin(t) graph has its first maximum at t= pi/2, and importantly it is symmetrical about a vertical line through t=pi/2.

    Now the graph you have been given is stretched along the x-axis.

    By symmetry, its maximum is half way between x= pi/5 and x=2pi/5, i.e. at x=3pi/10.

    So, the graph has been scaled along the x-axis to get pi/2 to 3pi/10.

    Can you see how to work out a from that?
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    (Original post by ghostwalker)
    I was hoping you'd post your diagram, otherwise I'm just going to have to assume it's correct.

    I am assuming that "a" is positive, though your question doesn't state that.

    The standard sin(t) graph has its first maximum at t= pi/2, and importantly it is symmetrical about a vertical line through t=pi/2.

    Now the graph you have been given is stretched along the x-axis.

    By symmetry, its maximum is half way between x= pi/5 and x=2pi/5, i.e. at x=3pi/10.

    So, the graph has been scaled along the x-axis to get pi/2 to 3pi/10.

    Can you see how to work out a from that?
    Hi, for some reason I can't post anything.
    Oh, and sorry, yes a is positive, and so is K
    I've done all of the above. So would the a in sin(ax)=k equal 3pi/5? Please?

    Thanks for a response
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    (Original post by MoniC255)
    Hi, for some reason I can't post anything.
    Oh, and sorry, yes a is positive, and so is K
    I've done all of the above. So would the a in sin(ax)=k equal 3pi/5? Please?

    Thanks for a response
    Not quite.

    In the standard graph you have sin(pi/2) = 1

    In your graph you have sin(a 3pi/10) =1

    So,

    a \dfrac{3\pi}{10}=\dfrac{\pi}{2}

    and solve for "a".
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    (Original post by ghostwalker)
    Not quite.

    In the standard graph you have sin(pi/2) = 1

    In your graph you have sin(a 3pi/10) =1

    So,

    a \dfrac{3\pi}{10}=\dfrac{\pi}{2}

    and solve for "a".
    Oh, I get it now! Thank you very much for your help!
 
 
 
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