This publication was done with the collaboration of Mauro Miguel de Jesús García Enríquez

Introduction

In past posts, we explored the behavior of the sine function with natural and real numbers in the argument, and now we're taking it to the next level!

What would result from combining random behavior with numbers distributed randomly? This was the question Mauro asked when we discussed a certain wave type and the previous post I wrote. In this post, we want to explore a particular type of numbers: Prime numbers.

The initial step is to examine the behavior of the sine wave, we have developed a series of functions that generate the sine function with prime numbers as parameters. These functions have been plotted with varying numbers of terms and domains to have a better understanding of the behavior where the argument has natural and real parameters. After obtaining a visual representation, the behavior is analyzed numerically. A table of the decimal behavior when the parameter of the sine function is an integer and a real number has been created. This table enables the examination of the behavior up to five decimal places. It also facilitates the determination of the values taken by the sine function at a certain point and the observation of the differences between them. In the final visual analysis, a comparison is made between the binary representation of the decimal numbers of the sine function, where the argument is natural and real, and where n ranges from 1 to 100. This allows for a comprehensive examination of the function's behavior.