Once, my two brothers, sin theta and cos theta visited me. By the way, I have a very close relationship with the theta family. I have known them from my school days.
They had read a funny post somewhere on Facebook, saying, “My whole life has gone by, but I don’t know where to use this sin theta and cos theta!”
It made them feel very sad. They told me to write something about it.
I said, “I will give it a try.”
After they both left, I had a flashback and I tried to remember what we had learned in school.
As such, sin theta -cos theta are very old and have been useful in geometry for ages. There is a lot of history behind both.
It all started with Optics. Snell’s law was taught while studying the refraction of light. It contained sin theta. As the study of light progressed, the theta brothers were found everywhere. These are there in both Diffraction and Interference. It would be impossible to study light without these two. Today we use many gadgets; we use binoculars; we use mobile cameras and DSLRs. The formulas that led to the creation of so many light-related inventions include sin theta and cos theta.
Later, we learned about the polarization of light. These two are again there on hand in explaining that principles formula. Goggles and screens are made based using concepts of this principle too. Being able to watch 3D movies is a gift of the brothers.
Newton’s laws were studied. When studying mass and force, both of them came up again. Later on, I got acquainted with Quantum Mechanics. Quantum mechanics is very popular. It is present in all the concepts of physics. Here too, theta brothers have their significance.
Today there are hundreds of places where Quantum Mechanics is used. From manufacturing our high-capacity mobile phones to various new materials, it would have been difficult without sin theta- cos theta. Both are present when studying the structure of atoms.
Later came Bragg’s Law while studying physics. This method (XRay Diffraction) is used to study the properties of a substance using X-rays. Sin theta came in handy to explain this also.
We see an immense expansion of electromagnetic science. Motors, generators, fans, vehicles, etc., have no alternative. And there is no substitute for sin theta-cos theta for the formulas in this domain.
Then we learned Fourier transforms. Today, the vast amount of data sent by satellites is compressed mathematically. In this sin theta-cos, theta has a place of honor.
Alternating Current (AC) is the electricity used in all our homes. In the field of electricity, these two are of utmost importance. From measuring the distance between two locations using latitude-longitude to calculating the orbit for launching a satellite into space, sin theta cos theta accompanies us everywhere.
Now talking about the healthcare field – when a doctor asks one to do an MRI scan; the two brothers are also involved in the nuclear magnetic resonance (NMR) program on which MRI is based. Thanks to them again.
The theta brothers are essential in the field of architecture too.
This list is never-ending. They are used from measuring the distances in space to atoms and molecules. Now, if someone asks you, where are sin theta and cos theta used in daily life? You know what to say, right? Hope my brothers’ usefulness to society is now known and they can feel happy again.