A Simple Application of a Trigonometric Inequality to the Relativistic Doppler Effect

In recent years, the special theory of relativity (SR) has been included in high school curricula in almost all countries. In addition to the classic demonstrations of the relativity of time and lengths, another interesting relativistic phenomenon that is shown, is the transverse Doppler effect. Obviously it is not possible to rigorously prove, at the high school level, the final relation but, from it, we have analyzed some physical consequences using trigonometry. In this paper, which has a didactic aim, we summarize one of our lessons held during some of the in-depth lectures on relativity that we often organize for high school students in our area.