Talk:Trigonometric tables

Unfortunately, that's not a useful algorithm for generating sine tables, for a number of reasons. It will only work as the number of divisions tends towards infinity, with infinite-precision arithmetic.

I might add more algorithms, Ive asked a guy about incorporating his page with four algorthms into wikipedia. /sandos

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(Has anyone ever actually used the Euler-integration method to compute trig tables?)

I would suggest dividing this article into a few sections:

• Historical computation of trigonometric tables, before computers were widespread. Who did it? What methods did they use? How accurately did they compute them?

• Recurrence algorithms used for FFTs, etcetera, summarizing the formulas that are most often used and their error characteristics.

• Stap —Preceding unsigned comment added by 77.238.193.253 (talk) 12:00, 27 September 2008 (UTC)

• Interpolation schemes that are used for employing tables to compute trig. functions of arbitrary arguments.

Probably, there should be a separate article on computing trigonometric functions, not necessarily tables per se, but how they are actually done in practice. (CORDIC algorithms, arithmetic-geometric mean techniques for arbitrary-precision arithmetic, etcetera.)

-- Steven G. Johnson

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Moved

Moved from the article:

To come

• Buneman's recurrence algorithm for accurate FFTs (Proc. IEEE 75, 1434 (1987)), or some similarly improved scheme (see Tasche, below).
• Calculating accurate approximations for trigonometric functions (CORDIC schemes, etcetera)
• Arbitrary-precision arithmetic methods (quadratically convergent schemes based on arithmetic-geometric mean, related to fast methods for computing pi)

— Timwi 16:24, 6 Mar 2004 (UTC)

Cool

You may please add some solved problems of trigonometry.{| class="wikitable" |- ! header 1 ! header 2 ! header 3 |- | row 1, cell 1 | row 1, cell 2 | row 1, cell 3 |- | row 2, cell 1 | row 2, cell 2 | row 2, cell 3 |}

The values of sine and cosine per every 675 seconds

$\cos(\alpha \pm \beta )=\cos \alpha *\cos \beta \mp \sin \alpha *\sin \beta \,\quad (Ac)$

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \sin(\alpha \pm \beta) = \sin\alpha*\cos\beta \pm \cos\alpha*\sin\beta\,\quad (As)}

$2\cos {\frac {\alpha \pm \beta }{2}}={\sqrt {2+2\cos(\alpha \pm \beta )}}\quad (Hc)$

$2\sin {\frac {\alpha \pm \beta }{2}}={\sqrt {2-2\cos(\alpha \pm \beta )}}\quad (Hc)$

$\,{\mbox{Fibonacci number 1.16180339... ≈ 2cos36°: }}$

${\mbox{2cos36° = 2sin54°}}={\frac {{\sqrt {5}}+1}{2}}=\phi ={\sqrt {1+\phi }}={\sqrt {2+{\frac {1}{\phi }}}}$

${\mbox{2sin36° = 2cos54°}}{\mbox{ ..................... }}={\sqrt {3-\phi }}={\sqrt {2-{\frac {1}{\phi }}}}$

${\mbox{2cos18° = 2sin72°}}={\mbox{ ................................. }}={\sqrt {2+\phi }}$

${\mbox{2sin18° = 2cos72°}}={\frac {{\sqrt {5}}-1}{2}}=\phi -1{\mbox{ ........ }}={\sqrt {2-\phi }}$

$\,{\mbox{The other well known values presented in same shape are: }}$

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \mbox{2cos90° = 2sin0°} = \mbox{ ........................... }= 0 = \sqrt{2 - \sqrt{4} } }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \mbox{2sin90° = 2cos0°} = \mbox{ ........................... } =2= \sqrt{2+\sqrt{4}} }

${\mbox{2cos30° = 2cos60°}}{\mbox{ ........................... }}={\sqrt {3}}={\sqrt {2+{\sqrt {1}}}}$

${\mbox{2cos60° = 2sin30°}}={\mbox{ .............................. }}1={\sqrt {2-{\sqrt {1}}}}$

${\mbox{2cos45° = 2sin45°}}{\mbox{ ........................... }}={\sqrt {2}}={\sqrt {2\pm {\sqrt {0}}}}$

$\,{\mbox{ Inserting these nine angles into (Ac) and (As) we get }}$
$\,{\mbox{the values of cosine and sine per every three degrees. }}$

${\mbox{2cos3° = 2sin87°}}={\sqrt {2-{\frac {\phi {\sqrt {3}}+{\sqrt {3-\phi }}}{2}}}}$

${\mbox{2sin3° = 2cos87°}}={\sqrt {2-{\frac {\phi {\sqrt {3}}+{\sqrt {3-\phi }}}{2}}}}$

$\,{\mbox{Half-angle formulae (Hc) and (Hs) applied 4 times give }}$
$\,{\mbox{the values of cosine and sine per every 675˝ i.e. 11´ 25˝:}}$
${\mbox{cos 675˝}}=\cos {\frac {\pi }{60*2^{4}}}={\frac {1}{2}}{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {2+{\frac {\phi {\sqrt {3}}+{\sqrt {3-\phi }}}{2}}}}}}}}}}$
${\mbox{sin 675˝}}=\sin {\frac {\pi }{60*2^{4}}}={\frac {1}{2}}{\sqrt {2-{\sqrt {2+{\sqrt {2+{\sqrt {2+{\frac {\phi {\sqrt {3}}+{\sqrt {3-\phi }}}{2}}}}}}}}}}$
$\,{\mbox{ The last is key factor of various Interpolation formulae. }}$
77.238.193.253 (talk) 21:30, 27 September 2008 (UTC)Stap