The article was created as the result of the research oriented at the innovation of the content and forms of teaching Mathematics at universities. The article contains a set of problems solved with the help of goniometric functions. These problems are not typical for school mathematics and while their solving it is necessary to use the connections with other branches of mathematics (solving binomial and reciprocal equations, Moivre´s theorem, Ptolemy´s theorem, arithmetic sequence, the theory of rational and irrational numbers, etc.). Solving these problems is the measure for deepening and widening of the secondary school and university students´ knowledge about trigonometric functions and contributes to their general mathematic overview.