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**vishalbhai****Member**- Registered: 2009-10-18
- Posts: 2

Hello!

Pls. help me find a way to calculate values like sin 5 & cos 10 ( the arguments are in degrees) without using tables or series...Just common formulas from grade 7-8 trignometry!!!

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

I can't think of any way using trigonometry formulas, but complex numbers numbers could be used to derive them.

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**vishalbhai****Member**- Registered: 2009-10-18
- Posts: 2

Thank you for the help!

Actually, I too did the same and got an equation of 3rd power with complex roots :-)

But the problem is, I need this for my daughter who is in class 8 and they haven't learned complex numbers as yet....

I think that the teacher made a mistake in the question paper - she wrote 5 instead of 15 :-)

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**Relatively Quantum****Member**- Registered: 2009-10-19
- Posts: 1

one word - calculator

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Using a calculator is indirectly using series, which isn't allowed in the question.

Since it's actually 15 though, it's easy enough to just use the half-angle formula on 30.

Why did the vector cross the road?

It wanted to be normal.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi;

Relatively Quantum has a point. Since some calculators (Texas Instruments- I think, I remember reading about it and HP) have abandoned Economized Taylor series and even Pade approximants in favor of that old Cordic algorithm which uses rotations to calculate. But it does need a table lookup initially so it violates one of his restrictions.

*Last edited by bobbym (2009-10-19 16:53:51)*

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi vishalbhai;

While looking for something else I found this page and remembered your post.

This guy is doing what we thought was impossible, Turned out Ptolemy and Archimedes solved this problem satisfactorily, without calculators or Taylor series, Pade approximants or Cordic. Just from knowing a few trig relations and some values of common angles. You should be able to get as close to sin(5°) as you wish,

http://www.marypat.org/stuff/nylife/010206.html

Just go past the first part that deals with Taylor series.

*Last edited by bobbym (2009-10-31 21:35:23)*

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**betterthangauss****Member**- Registered: 2009-10-31
- Posts: 11

The following recursive algorithm will do it without any table lookup, and could be done by hand without having to do anything but multiply, subtract, and divide

It should be pretty fast, since dividing by 3 on each step will drop the argument to arbitrarily small size in logarithmic time. Of course, don't compute sin(x/3) twice in every iteration!

Here's a proof that it works:

*Last edited by betterthangauss (2009-11-01 00:13:05)*

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**Sarah12****Guest**

Thats Geometry.:cool:

**mehehhe****Guest**

meheheheheheh:):|:(:D:o;):/:P:lol::mad:::cool:

P.S.

IDK i drag at math

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi;

Why? Have you tried as hard as you could?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Hmm.....Without a series or a table?

Does such formula exist?

Well, I suggest this method (an Impossible and stupid one):

`Draw a right angled triangle with :theta = 5, and find the ratio of the Perpendicular and Hypotenuse`

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

That idea is actually not so goofy anymore. You could use geogebra!

**In mathematics, you don't understand things. You just get used to them.**

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Of Course , But what should be the real solution?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,879

Hi Agnishom;

There is a link in post #7 and the post #8 looks promising.

**In mathematics, you don't understand things. You just get used to them.**

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