Year 13 Maths Help Thread

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    (Original post by kiiten)
    is it because its a stretch in the y-direction, scale factor 3?
    Yep, that's better.
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    (Original post by kiiten)
    y=4+3sin(2x-1)

    is the amplitude of this sine wave 3 because the sin has a 3 in front of it?
    If in doubt, check the definition of amplitude and then sketch the graph, but I think you should be okay.
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    (Original post by RDKGames)
    Yep, that's better.
    If the 3 wasnt there would it just be 1?

    Also for the same sine wave the phase shift is -1.Is this because it is translated by [1 0] to the right?
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    (Original post by kiiten)
    If the 3 wasnt there would it just be 1?

    Also for the same sine wave the phase shift is -1.Is this because it is translated by [1 0] to the right?
    Yes if the 3 wasn't there it would be 1.

    Shift where? sin(x-a)+b is a translation by vector [a,b].

    EDIT: Oh sorry, for more general case, sin(ax-b)+c=sin[a(x-\frac{b}{a})]+c is a translation by vector [\frac{b}{a},c] alongside a stretch of \frac{1}{a} in the x direction.
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    (Original post by RDKGames)
    Yes if the 3 wasn't there it would be 1.

    Shift where? sin(x-a)+b is a translation by vector [a,b].

    EDIT: Oh sorry, for more general case, sin(ax-b)+c=sin[a(x-\frac{b}{a})]+c is a translation by vector [\frac{b}{a},c] alongside a stretch of \frac{1}{a} in the x direction.
    So why is the phase shift for the sine wave 4+3sin (2x-1) just -1?
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    (Original post by kiiten)
    So why is the phase shift for the sine wave 4+3sin (2x-1) just -1?
    It's not? The horizontal translation is 1/2.
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    (Original post by RDKGames)
    Yes if the 3 wasn't there it would be 1.

    Shift where? sin(x-a)+b is a translation by vector [a,b].

    EDIT: Oh sorry, for more general case, sin(ax-b)+c=sin[a(x-\frac{b}{a})]+c is a translation by vector [\frac{b}{a},c] alongside a stretch of \frac{1}{a} in the x direction.
    You say a translation alongside the stretch, but it's worth saying which one is first because the order of performing each transformation matters.
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    (Original post by B_9710)
    You say a translation alongside the stretch, but it's worth saying which one is first because the order of performing each transformation matters.
    True.

    It's either a translation by vector [b,c] followed by a stretch of factor 1/a in the x-direction.
    Or a stretch of factor 1/a in the x-direction followed by a translation by vector [\frac{b}{a},c]

    Still neither case fits the -1 in her question.
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    (Original post by RDKGames)
    True.

    It's either a translation by vector [b,c] followed by a stretch of factor 1/a in the x-direction.
    Or a stretch of factor 1/a in the x-direction followed by a translation by vector [\frac{b}{a},c]

    Still neither case fits the -1 in her question.
    Yeah thats why im confused because it says the phase shift is -1 - unless my teacher made a mistake or phase shift means something else?

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    (Original post by kiiten)
    Yeah thats why im confused because it says the phase shift is -1 - unless my teacher made a mistake or phase shift means something else?

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    Must be a mistake; it's definitely not a minus number, it could be a +1 instead depending on the order of transformation. Phase shift is how much it moves horizontally to the right of the usual position.

    So in your case, +1 would make sense for sin(2x-1) if sin(x) was firstly translated by vector [1,0] \mapsto sin(x-1) and then stretched in the x-direction by a factor of \frac{1}{2} \mapsto sin(2x-1)

    It would be +1/2 if the stretch came first followed by the shift.
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    (Original post by RDKGames)
    Must be a mistake; it's definitely not a minus number, it could be a +1 instead depending on the order of transformation. Phase shift is how much it moves horizontally to the right of the usual position.

    So in your case, +1 would make sense for sin(2x-1) if sin(x) was firstly translated by vector [1,0] \mapsto sin(x-1) and then stretched in the x-direction by a factor of \frac{1}{2} \mapsto sin(2x-1)

    It would be +1/2 if the stretch came first followed by the shift.
    So, if the shift came first before the stretch it would be +1?
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    (Original post by kiiten)
    So, if the shift came first before the stretch it would be +1?
    Yes. I assume you've learnt about order of transformation in C3 and how it's important, otherwise this can seem confusing.
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    (Original post by RDKGames)
    Yes. I assume you've learnt about order of transformation in C3 and how it's important, otherwise this can seem confusing.
    Unless thats one of the first C3 topics then no i dont think ive learnt that yet?
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    (Original post by kiiten)
    So, if the shift came first before the stretch it would be +1?
    Think about it. If we have  f(x)=\sin 2x and we translate it 2 units to the right then this is given by  f(x-2)=\sin (2(x-2)) = \sin (2x-4) .
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    (Original post by kiiten)
    Unless thats one of the first C3 topics then no i dont think ive learnt that yet?
    It should be a C3 topic, one of the early ones too. Besides, that type of question can't just blatantly ask for a horizontal translation without specifying in which order the transformations happen.
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    How do you go about drawing this sine wave: y=4+3sin(2x-1)

    Also i came across a similar question which asks for the phase shift of 5+2sin(2x+1). The answer is 1??
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    (Original post by kiiten)
    How do you go about drawing this sine wave: y=4+3sin(2x-1)

    Also i came across a similar question which asks for the phase shift of 5+2sin(2x+1). The answer is 1??
    To sketch it, well you know the translations, the stretches, and you can find the stationary points via differentiation which should give you enough info to sketch it. Set yourself a region for it, like between 0 and 2pi which should be enough.

    And no, it would be -1 if the translation came before the stretch for that one.
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    Hw dyu integrate
    asinbx
    like if a and b were proper numbers then i can do it but like they r letters so im not sure.
    Zacken anyone can u help please.



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    (Original post by physicsmaths)
    Hw dyu integrate
    asinbx
    like if a and b were proper numbers then i can do it but like they r letters so im not sure.
    Zacken anyone can u help please.



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    If you can do it with numbers then im sure you can figure out the letters...


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    (Original post by RDKGames)
    If you can do it with numbers then im sure you can figure out the letters...


    Posted from TSR Mobile
    No. It is impossible 100% cause what tf is the letters doing there nothing bruv nothing.


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