2012 Maths Paper Problem :L (1 Viewer)

ebbygoo · Jul 28, 2013

Hey guys.

Just studying for trials, and was doing the 2012 Mathematics Paper.
All was going well, getting all the answers right and then BAMN.
I get to Q16.
Part b- i and c I don't get them at all :L
I looked at the sample answers, and they dont help either. For example, in part b, how the hell did they just randomly get to suddenly having the co ordinates of T as (cosx, sinx) :L

Anyone ????

SpiralFlex · Jul 28, 2013

$i) Thought processes: We are required to find equation$\; PT. \;$Now, notice that\; $PT$\; is tangential to the circle. Does this remind you of something? Calculus? Maybe we can differentiate as we may do but there is a term involving$ \;y,\; $we haven't learnt how to differentiate implicitly yet. So we seek a better method.$

$What about this? Try and find the coordinates of$\; P\; $and maybe$\; T.\; $Can we construct a equation from that? It seems reasonable. Can you do this? Can you see why the point$\; T\; $has coordinates$\; T(\cos \theta, \sin \theta).\; $Drop a perpendicular from$\; T. \;$We also know that$\; OT = 1. \;$(Why?)$

I will help you with the rest, once you have completed i)

ebbygoo · Jul 28, 2013

I got the rest of b, just used the equation. I just can't see how you get the coordinates of T.
And then yeah no idea on c. Tried finding point of intersection, but don't get why it would be useful.

SpiralFlex · Jul 28, 2013

I defined a point S for Spiral here.

$\cos \theta = \frac{OS}{1}$

$OS=\cos \theta$

$\sin \theta = \frac{ST}{1}$

$ST=\sin \theta$

$T(\cos \theta, \sin \theta)$

SpiralFlex · Jul 28, 2013

ebbygoo · Jul 28, 2013

Thanks I get part b now

Ill look at c again soon.

2012 Maths Paper Problem :L (1 Viewer)

ebbygoo

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SpiralFlex

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ebbygoo

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SpiralFlex

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SpiralFlex

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ebbygoo

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