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    June 2013 Q8, here is the paper; http://qualifications.pearson.com/co...e_20130621.pdf page 24 of the pdf

    and my working;

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    what is the significance of the  \displaystyle  \sin\theta = 0 and  \displaystyle \sin\theta = -\sqrt\frac{2}{3} ?

    do they tell you anything about the plot or do you just neglect them by realising the angle required is roughly equal to  \displaystyle \frac{\pi}{4}

    (kind of like how in mechanics projectiles when using  \displaystyle s = ut + \frac{1}{2}at^2 to find t you sometimes get the minus t value which you usually ignore)
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    dont think it has any real significance in this case, other than that the curve also meets the half line at the origin
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    (Original post by DylanJ42)
    do they tell you anything about the plot or do you just neglect them by realising the angle required is roughly equal to  \displaystyle \frac{\pi}{4}
    Although it's not obvious from the diagram, \sin \theta =  0 gives a point where the tangent is parallel to the initial line, but it's actually the origin. We discard it as the requirement is P is distinct from O.

    The other value of theta will also give rise to a line parallel to the initial line, but it's outside the domain of the definition of C, so we can again discard it.
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    (Original post by drandy76)
    dont think it has any real significance in this case, other than that the curve also meets the half line at the origin
    PRSOM

    (Original post by ghostwalker)
    Although it's not obvious from the diagram, \sin \theta =  0 gives a point where the tangent is parallel to the initial line, but it's actually the origin. We discard it as the requirement is P is distinct from O.

    The other value of theta will also give rise to a line parallel to the initial line, but it's outside the domain of the definition of C, so we can again discard it.
    i've never realised that the tangent was parallel to initial line at the origin ever, i always thought it was a mysterious recurring solution which we ignored "just because" and i never understood why :laugh:, but this all makes complete sense now

    thank you both
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    If  r \rightarrow 0 as  \theta \rightarrow a then  \theta = a is a tangent to the curve.
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    (Original post by B_9710)
    If  r \rightarrow 0 as  \theta \rightarrow a then  \theta = a is a tangent to the curve.
    is this what is happening at the origin?

    if i was to zoom in really close...

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    would  \displaystyle \theta = \frac{\pi}{2} be a solution to  \displaystyle \frac{dx}{d\theta} with that same reasoning
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    (Original post by DylanJ42)
    is this what is happening at the origin?

    if i was to zoom in really close...

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    would  \displaystyle \theta = \frac{\pi}{2} be a solution to  \displaystyle \frac{dx}{d\theta} with that same reasoning
    yeah, comes up a lot in OCR as a precursor to finding area bound by the curve, since the tangents at the origin can be taken as the limits
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    (Original post by drandy76)
    yeah, comes up a lot in OCR as a precursor to finding area bound by the curve, since the tangents at the origin can be taken as the limits
    exactly yea you're right, i always know to take limits from 0 to pi/2, so i guess it follows that tangents exist at 0 and pi/2
    Spoiler:
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    you know when you sometimes feel like you shouldn't be doing further maths.. yeaa now is one of those times
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    (Original post by DylanJ42)
    exactly yea you're right, i always know to take limits from 0 to pi/2, so i guess it follows that tangents exist at 0 and pi/2
    Spoiler:
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    you know when you sometimes feel like you shouldn't be doing further maths.. yeaa now is one of those times
    Dw about it just probs not covered in your syllabus, for instance I never know what's going on when people mention conics


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    (Original post by drandy76)
    Dw about it just probs not covered in your syllabus, for instance I never know what's going on when people mention conics
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    yea i guess, i know it now and that's the main thing thanks again :cute:
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    (Original post by drandy76)
    Dw about it just probs not covered in your syllabus, for instance I never know what's going on when people mention conics


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    :zomg:
 
 
 
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