A Most Elegant Equation by David Stipp

Author:David Stipp
Language: eng
Format: epub
Publisher: Basic Books
Published: 2017-11-07T05:00:00+00:00

cos 0.663 = 1 − (0.663)2/2! + (0.663)4/4! − (0.663)6/6! + (0.663)8/8! + ….

Adding up the first five terms in the infinite sum yields cos 38o ≈ cos 0.663 radians ≈ 0.788. Happily, my calculator’s estimate of cos 38o agrees with this.

Plugging in 0.663 for the angle in the sine equation’s first five terms gives

sin 0.663 = 0.663 − (0.663)3/3! + (0.663)5/5! − (0.663)7/7! + (0.663)9/9!.

Adding up the terms on the right side of the equals sign yields sin 38o ≈ sin 0.663 radians ≈ 0.616—further reassuring agreement with my calculator.

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