Understanding the "waves" of events

Just the other day, I was working with one of my young students to determine the function formula when either the cos or sin graph was provided. If many of you are not very familiar with sin/cos graphs please check them because they are used in many applications. Some examples are music waves, space flights, signal transmissions etc. (https://en.wikipedia.org/wiki/Trigonometric_functions)

But the topic is less mathematical and more about our daily work life events and their interpretation. We are the function (y) and all of the events are nothing more than x’s. We can see how we respond to different events and yet not all the time we can act before something is happening. The question is why not?

If we understand the input(s) and can see how the distribution is happening, why is it that we can not determine the function equation? We can see how things are translated and shifted, how the waves will take us either up or down, yet we can not determine the formula. You might ask on why the formula is important to know? The answer is that without a formula we will not be able to predict what will happen. The prediction might not be ideal yet it gives us the balance that we are in control of the future events rather than the events are being in control.

Now, when we have a formula and numbers associated, it is easier to draw the graph because all that we need to do is to input the amplitude, range, phase shift and vertical shift. But we, can visualize the graph through our senses yet, we do not know what will happen next because we have no formula. Our senses are moving us and shifting us and yet we do not know the numbers for periodicity or amplitude or where the next shift will happen so we can prevent if anything wrong ought to happen.   

It became more difficult because the only way we will be able to determine the period is by being patient and seeing when the function becomes stable….this is time that will give us the indication of whether we reached stability or not.

The stability is harder to observe and determine when there are more events happening at different frequencies therefore from practical experience, we will need to wait until the noisy waves will calm down and separate the events such that we only observe one unknown rather than many unknowns.

Only when a process becomes relatively stable we can determine the formula function. Caution, it will only happen for a determined period of time,  so do not miss the opportunity.