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Sine of multiples
The general formula for calculating the sine of multiples is
Explanation
We start with
Let y = y + z then you get
For x = y = z it follows
There seems no clear structure in that. Because both sin0x = cos0x = 1 you can expand all terms by this factor
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We try to find some kind of Pascal's triangle. Because of that, we add by brute force terms with braces { }, which must eventually disappear
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If we now also add a factor that is alternately 0, 1, 0, −1 and so on, it is solved. Therefore we can write Vieta's formula for calculating the sine of multiples as
HistoryThe formula was given by the French mathematician François Viète (1540 - 1603). |