Usage of cotg; Area of polygon

**Zellator** · June 14th 2011, 04:11 AM

Hi Forum
Here is a question

$A=[ns^2 cotg (\pi/n)]/4$

I am confused about the usage of cotg in this formula. How was this formula calculated?

If we use only tg we'd get
$na^2tan(\pi/n)$

This $\pi/n$ angle regards the angle of the side $s$ , correct?

I'm no pro in co-trigonometric functions but,
Will this, in any way, relate to the fundamental propriety of cotg=A/O?
Trigonometric functions on non right angles are rather strange.

Thanks.

**Plato** · June 14th 2011, 06:02 AM

Originally Posted by Zellator

Hi Forum
Here is a question

$A=[ns^2 cotg (\pi/n)]/4$
I am confused about the usage of cotg in this formula. How was this formula calculated?

If we use only tg we'd get
$na^2tan(\pi/n)$

This $\pi/n$ angle regards the angle of the side $s$ , correct?

No that is not correct.
$\Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
Thus we have $\cot (\Theta ) = \frac{{2a}}{s}$ .
Note that $a$ is the length of the altitude and $s$ is the length of the base.

**Zellator** · June 14th 2011, 09:09 AM

Originally Posted by Plato

$\Theta = \frac{{2\pi }}{n}$ is the central angle of a regular polygon.
Thus we have $\cot (\Theta ) = \frac{{2a}}{s}$ .
Note that $a$ is the length of the altitude and $s$ is the length of the base.

Hi Plato
I guess I didn't know how to put the central angle part in proper terms. Thanks for the explanation.
Though I'm kind of confused of where does the 2 in $a$ comes from.

Maybe we have a two there because $s$ is actually $\frac{{s}}{2}$ ?

Ok this was very confusing before your explanation.
I hope I got it right!
Thanks again Plato!

Thread: Usage of cotg; Area of polygon

LinkBack

Thread Tools

Display

Usage of cotg; Area of polygon

Re: Usage of cotg; Area of polygon

Re: Usage of cotg; Area of polygon

Similar Math Help Forum Discussions

Polynomial, area of a polygon

Find the area of the polygon

Area of Polygon with integrals

Area of a polygon

Area of a Regular Polygon

Search Tags