metalslayer
  • metalslayer
A regular n-gon is inscribed in the unit circle. What is the perimeter for each n below? a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Aye, mate. I may be of some assistance. But first, I need a favor from ye. Tell me when the observatory is.
metalslayer
  • metalslayer
What observatory?
metalslayer
  • metalslayer
I really need help on this

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geerky42
  • geerky42
Do you know Trigonometry? Or at least Law of Cosines?
geerky42
  • geerky42
If so, this site may helps: http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/lindsay2.html
metalslayer
  • metalslayer
I've been on that website. I just don't get it. Can you please just solve for A and show the steps so I could do the rest? Thanks.
metalslayer
  • metalslayer
I do know trig and law of cosines and sines
geerky42
  • geerky42
What A?
metalslayer
  • metalslayer
a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?
metalslayer
  • metalslayer
Please show me how to answer some of them with the steps. Thank You.
metalslayer
  • metalslayer
By A i meant n=3
geerky42
  • geerky42
From site, our equation would be \(P = nc = n\sqrt{2-2\cos\left(\dfrac{360^\text o}{n}\right)}\)
geerky42
  • geerky42
Do you understand how this equation was derived?
metalslayer
  • metalslayer
P is perimeter, n is the n-gon, what is c?
geerky42
  • geerky42
c is side.
metalslayer
  • metalslayer
How do I find the side? I am only given the n.
geerky42
  • geerky42
You can use law of cosines to find the length of sides:|dw:1436579931950:dw|
geerky42
  • geerky42
n-gon is inscribed in unit circle, which has radius of 1.
metalslayer
  • metalslayer
So lets try to solve a.) n=3. I will plug in n into 360/n so it will equal 120 degrees. Then I have no idea lol.
geerky42
  • geerky42
Yes, Plugging in n=3, you would have \(P = 3\sqrt{2-2\cos\left(120^\text o\right)}\)
geerky42
  • geerky42
You can just use calculator.
metalslayer
  • metalslayer
p=5.2?
geerky42
  • geerky42
Yeah I got approximately that.
metalslayer
  • metalslayer
So first I divide 360 by n, and then plug it into the formula?
geerky42
  • geerky42
Actually, you just plug in whether value of n, then calculate.
geerky42
  • geerky42
For case of n=3, you just plug in n=3 and calculate \(P = 3\sqrt{2-2\cos\left(\dfrac{360^\text o}{3}\right)}\)
metalslayer
  • metalslayer
Oh I see. Thank you. What about if n = 542?
geerky42
  • geerky42
Same. Plug in n=542 then calculate \(P = \textbf{542}\sqrt{2-2\cos\left(\dfrac{360^\text o}{\textbf{542}}\right)}\)
metalslayer
  • metalslayer
Great, thanks. And lastly could you please explain part h.
metalslayer
  • metalslayer
h. The perimeter in part f should be close to what number? How close is it?
geerky42
  • geerky42
Well, imagine if n goes to infinity, what would n-gon become into?
metalslayer
  • metalslayer
a circle
geerky42
  • geerky42
Right. Saying we have case of \(n=\infty\). How can we find perimeter?
geerky42
  • geerky42
Or should I say "circumference"?
metalslayer
  • metalslayer
\[\pi radius squared\]
metalslayer
  • metalslayer
pi radius squared
geerky42
  • geerky42
That's area of circle. We want circumference.
metalslayer
  • metalslayer
2pi*r
metalslayer
  • metalslayer
so what is the radius?
geerky42
  • geerky42
Yeah. Here, we have UNIT circle, so radius is 1. So part f should be close to \(2\pi\)
metalslayer
  • metalslayer
So that's my answer? Thank You. You are so helpful.
geerky42
  • geerky42
Yeah. Though I am not sure how to answer "How close is it?" I guess subtract part f from \(2\pi\).
geerky42
  • geerky42
But I think you did your job good enough lol...
metalslayer
  • metalslayer
Thank you. This helped me so much.

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