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In this paper, algorithms and architectures for the evaluation of trigonometric functions in the Logarithmic Number System (LNS) are described. A novel algorithm for the computation of the LNS cosine, based on the subtraction function, is presented and extended to compute all trigonometric functions. The proposed algorithms show a major advantage over other methods in terms of memory requirements (up to 94% improvement as opposed to direct polynomial approximation) and computational speed. A hardware implementation of an. elementary LNS trigonometric processor with 12-bit accuracy is also presented, to illustrate the feasibility of extending the LNS processors to include trigonometric functions.