how to find the sum of sines whose angles are in A.P.

gourish · 2014-05-27 20:15:14

i need to find out the formula to find the sum of sines whose angles are in A.P. in as many ways as i can... can anybody help me?

P.S. i should be apply such techniques to find the sum of cosines or tangents whose angles are in A.P.

Bob · 2014-05-27 20:24:09

hi gourish,

I'm in a rush but here's a possible start; I'll look in later to see if that has worked for you.

Let the angles be A, B and C.

If they are in AP then

A + d = B
B + d = C

therefore

A - B = B - C

A + C = 2B

But we also know they add to 180 degrees so you can work them out.

Bob

gourish · 2014-05-27 20:28:54

we have this series sin a + sin a+d + sin a+2d + sin a+3d+.......+sin a+(n-1)d = [sin (nd/2) sin{a+(n-1)d/2) ] over sin (d/2)... this is given in my book... but i don't trust them i want to find out the answer to this series on my own... and the angles need not necessarily add up to 180 degree.... bob can you give any advice on this? a quick one if you are in a hurry

Agnishom · 2014-05-27 22:03:00

Even if you cannot prove it, verify it to some extent using a calculator and a computer.

Bob · 2014-05-27 22:16:12

sorry gourish,

I'd just helped someone with a triangle question, so I made a mistake reading yours.

I'll try again.

Bob

Agnishom · 2014-05-27 22:18:57

Hahaha...

Bob · 2014-05-28 01:31:45

Haha indeed. Show a little respect for an old man who's going senile.

I haven't done it but I can get you some of the way.

Here's a factor formula:

If you pair up successive terms it quickly gets very messy, but if you pair the first with the last; and the second with the second from last; etc etc you'll find a common factor appearing that is one of the required bits in the answer.

Snags:

How do you allow for a possible middle term with no pair?

What do you do with the cosine terms that are left?

Maybe use another factor formula?

That's all for now.

Bob

gourish · 2014-05-28 02:13:18

thanks bob... appreciate it i will work on the problem following your advice....

gourish · 2014-05-28 20:34:15

i am still stuck with it i don't see any relevance other then the sin {a+(n-1)d/2} that comes in the sum of sines i am not getting to the proof....

Bob · 2014-05-28 22:33:09

hi gourish,

Can you do Latex? Post up where you've got to and I'll have a further look.

Bob

Math Is Fun Forum

#1 2014-05-27 20:15:14

how to find the sum of sines whose angles are in A.P.

#2 2014-05-27 20:24:09

Re: how to find the sum of sines whose angles are in A.P.

#3 2014-05-27 20:28:54

Re: how to find the sum of sines whose angles are in A.P.

#4 2014-05-27 22:03:00

Re: how to find the sum of sines whose angles are in A.P.

#5 2014-05-27 22:16:12

Re: how to find the sum of sines whose angles are in A.P.

#6 2014-05-27 22:18:57

Re: how to find the sum of sines whose angles are in A.P.

#7 2014-05-28 01:31:45

Re: how to find the sum of sines whose angles are in A.P.

#8 2014-05-28 02:13:18

Re: how to find the sum of sines whose angles are in A.P.

#9 2014-05-28 20:34:15

Re: how to find the sum of sines whose angles are in A.P.

#10 2014-05-28 22:33:09

Re: how to find the sum of sines whose angles are in A.P.

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