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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




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Topic review (newest first)

2012-11-10 15:19:23

Hi Agnishom;

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

2012-11-10 13:48:18

Of Course wink , But what should be the real solution?

2012-11-10 08:21:34

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

2012-11-10 02:52:21

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

big_smile tongue

2012-11-09 09:17:51


Why? Have you tried as hard as you could?

2012-11-09 09:15:45

roflol meheheheheheh:)neutralsadbig_smileyikeswinkhmmtonguelolmadrollcooldizzyeekkisskissrolleyesshamedownuptouchedsleepwavesweartonguewhatfaintdunno

IDK i drag at math

2009-11-07 05:42:42


2009-11-01 23:10:34

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:

2009-11-01 20:30:47

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,

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

2009-10-20 15:42:51


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.

2009-10-20 03:06:51

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.

Relatively Quantum
2009-10-20 02:52:07

one word - calculator

2009-10-19 19:02:40

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 :-)

2009-10-19 01:34:27

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

2009-10-19 00:25:38

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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