HSC Stuff > HSC Mathematics Advanced
Help with 2015 Independent Math Trial Paper (again)
jamonwindeyer:
--- Quote from: RuiAce on July 24, 2016, 01:25:19 am ---This one was really really dodgy. I promise if nobody gets an answer in then I will delete this post and replace it with an answer tomorrow.
--- End quote ---
In the interests of honesty I won't have time to sit down and tackle this properly until Sunday evening ;D
As some guidance (not a proper written solution) for the poster, the first question is using the area of a triangle formula:
Both a and b are your radii, and notice this as well (by double angle formula for sine, this is an extension paper right?):
So, to match the result in the question, you just need to prove that the angle in the middle is:
This comes directly from the properties of a regular polygon. Think about the triangular slices of a hexagon, for example. There are six of them, so each angle at the centre is 360/6=60 degrees. For n sides, it is 360/n degrees at the centre. Apply this principle to radians and your answer comes out!
To find the similar expression, you'll use a similar idea, but there will be an extra trick to it. Can't spot it right this second (2am might be a bit late to be doing Math ;)) but Rui may be able to enlighten. The last part will simply be dividing the two answers and maybe (probably) using a Pythagorean identity or something similar (must be something to it for 2 marks) ;D This might get you started!! ;D
joey9911:
Thanks Jamon for the help! I still don't know how to do it, so I might wait till RuiAce comes up with an answer (If he is willing to!) :D
And this was the last question in the 2unit 2015 Mathematics Independent Trial Paper, not Extension 1. All of my friends said this last question was fit for Extension 1 students only, (they need help with it too), so I don't know why a question this hard is in a 2u paper :\
RuiAce:
No no no this can definitely be done by 2U methods only.
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joey9911:
Wow! Thank you so much!
I just have a one question from your amazing solution.
For the area of the second triangle, A2-O-N, why are the angles 2pi/n? If it's the same area, same angle, shouldn't it be pi/n?
Thanks again!
RuiAce:
--- Quote from: joey9911 on July 24, 2016, 11:06:36 am ---Wow! Thank you so much!
I just have a one question from your amazing solution.
For the area of the second triangle, A2-O-N, why are the angles 2pi/n? If it's the same area, same angle, shouldn't it be pi/n?
Thanks again!
--- End quote ---
After I finished my solution, I realised that I made heaps of typos. Tried getting rid of all of them but it seems I missed that one! I'll edit it now
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