**5. Conclusions**

In this paper, we have identified several properties of *q*-cosine Euler polynomials and *q*-sine Euler polynomials. In addition, the relationship between polynomials was confirmed according to the various conditions of the variables. We were able to assume the structure of the approximate roots of the *q*-cosine Euler polynomials and the *q*-sine Euler polynomials and finally, produce some speculations. The structure of the approximate roots will come out in various ways depending on the condition of the variables, and new methods and theorems related to approaching this needs to be created and proved.

**Author Contributions:** Conceptualization, J.Y.K.; Data curation, C.S.R.; Formal analysis, C.S.R.; Methodology, J.Y.K.; Software, J.Y.K.; Writing—original draft, J.Y.K. These authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (No. 2017R1E1A1A03070483).

**Acknowledgments:** The authors would like to thank the referees for their valuable comments, which improved the original manuscript in its present form.

**Conflicts of Interest:** The authors declare that there is no conflict of interests regarding the publication of this paper.
