An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. lThe method is based on zero isolation techniques for algebraic polynomials. An efficient method for the calculation of the coefficients of a corresponding algebraic polynomial is stated. The complexity of trigonometric zero isolation depending on the degree and the coefficient size of the given trigonometric polynomial is analyzed. In an experimental evaluation, the performance of the method is compared to the performance of recently developed numeric techniques for the approximate determination of all roots of trigonometric polynomials. The case of exponential or hyperbolic polynomials is treated in an appendix.

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