Further closed forms for finite sums of weighted products of the sine and cosine functions

Publication Type:
Journal Article
Fibonacci Quarterly, 2018, 56 (1), pp. 38 - 42
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© 2018 Fibonacci Association. All rights reserved. In this paper, we present closed forms for six families of finite sums of weighted products of the sine/cosine functions. In each finite sum that we define, the summand contains a product of trigonometric functions, and the length of this product can be made as large as we please. A special case of one of our main results is the sumi=1n2 cos12icos i cos(i − 3) = cos 1 −cosn cos(n + 1) . 2ncosn2 Here the weight term in the summand is2 cos12i.
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