I'm currently studying the trigonometry behind biorhythms. I was reading through the Wikipedia article on the topic (https://en.wikipedia.org/wiki/Biorhythm) which states that:
Basic arithmetic shows that the combination of the simpler 23- and 28-day cycles repeats every 644 days (or 1-3/4 years), while the triple combination of 23-, 28-, and 33-day cycles repeats every 21,252 days (or 58.18+ years).
From my understanding, these are instances where they intersect on the x axis, but I may be mistaken.
What I am looking for are the points in time when two and three of the sine waves intersect and do so exactly when intercepting the x axis (x, 0). These are refered to as "double critical" and "super critical" days respectively. I have read articles and watched videos explaining how to find intercepts of sine waves, but I am unable to find an explaination as to how this can be used when a particular coordinate is wanting to be found.
The equations for the three waves are as follows:
- Physical: $\sin(2πx/23)$
- Emotional: $\sin(2πx/28)$
- Intellectual: $\sin(2πx/33)$
All the waves start at the point (0,0) at the date of birth. For consistancy, let's make that 1/1/1970.
Would someone be able to explain the process required to solve this?
Thank you in advance,