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For example, consider a supermarket with 1000 products and two customers. The basket of the first customer contains salt and pepper and the basket of the second contains salt and sugar. In this scenario, the similarity between the two baskets as measured by the Jaccard index would be 1/3, but the similarity becomes 0.998 using the SMC.
In mathematics, the Jacobi–Anger expansion (or Jacobi–Anger identity) is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is useful in physics (for example, to convert between plane waves and cylindrical waves), and in signal processing (to describe FM signals).
The Tatra 815-7 (also known as Tatra 817, T817 or Tatra Force) is a heavy army logistics vehicle made by the Czech company Tatra produced since 2007. T817 is primarily intended for military operators and for specialist roles in civilian sector (with Tatra 158 Phoenix being the company's primary general-purpose truck for civilian sector).
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Personal computer (PC) users are much less sensitive to product rank. [19] That is, they add more products to their evaluation pool before deciding on a product. This suggests that the cognitive effort it takes to process information, and thus the search costs, are much higher when users access the internet through their mobile phones. [19]
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions.Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated.
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...