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Viète's infinite product

The sinus cardinalis can be written as an infinite product

 

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Explanation

We start with the addition formula for the sine in the form

and eventually we get

Now we divide by a and get

In parentheses is a limit with the sine, which has the value 1. So we may write

 

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History The French mathematician François Viète (1540 - 1603) developed this infinite product.

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