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#1 2016-08-06 02:07:41

jacks
Member
Registered: 2012-11-21
Posts: 132

Trigonometric sum

If

Then
is

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#2 2016-08-07 04:47:31

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Trigonometric sum


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#3 2016-08-07 16:35:33

jacks
Member
Registered: 2012-11-21
Posts: 132

Re: Trigonometric sum

Yes thickhead right answer, Would you like to explain me.

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#4 2016-08-07 19:12:38

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: Trigonometric sum

hi jacks,

Yes, I got that value to, just by calculation in Excel.  But I guess you want an analysis of how to get this by algebra etc.  I've been working on this, on and off,  for two days and haven't got a method yet.  My first attempt was to try and simplify the trig. using various trig. identities.  Just went round in circles with that.  Then I made a diagram with a 14 point polygon inscribed in a circle, and tried to find a method using the distances in right angled triangles plus similar triangles, angles in semi circle etc.  I think that is the way to go with this, but a solution still alludes me.  If I still cannot get anywhere by the end of today, I'll post my diagram.  Maybe someone else can spot what I'm missing.  sad

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2016-08-07 21:40:32

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Trigonometric sum

Last edited by thickhead (2016-08-07 22:10:27)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#6 2016-08-08 02:12:26

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: Trigonometric sum

hi thickhead,

Wow!  Excellent proof.  I would never have thought of that.  Have a gold medal:

UodvFYx.gif

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2016-08-08 02:37:20

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Trigonometric sum

Thank you ,bob bundy.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#8 2016-08-08 14:04:31

jacks
Member
Registered: 2012-11-21
Posts: 132

Re: Trigonometric sum

Thanks thickhead nice solution using complex number

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