Math Is Fun Forum

jacks

Member

Registered: 2012-11-21

Posts: 132

Trigonometric sum

If

Then

is

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Trigonometric sum

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{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.}

jacks

Member

Registered: 2012-11-21

Posts: 132

Re: Trigonometric sum

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

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. 

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Trigonometric sum

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

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{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.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Trigonometric sum

hi thickhead,

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

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Trigonometric sum

Thank you ,bob bundy.

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{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.}

jacks

Member

Registered: 2012-11-21

Posts: 132

Re: Trigonometric sum

Thanks thickhead nice solution using complex number