Sine & Cosine
“Anything will give up its secrets if you love it enough” — George Washington Carver
Sine, Cosine and their first cousin, Tangent tormented me for a long time in secondary school. I avoided them like a plague. Let me put it in context, I avoided them like ebola. Yes, I did put in the effort to avoid them. I just could not wrap my head around the concepts that governed them. I gave it one more try and gave up.
As I progressed through the ranks and with a year left before I took the final exams in secondary school, it became crystal clear to me that I was deceiving myself and eluding the obvious. The truth was that I needed to understand this concept. It ran through almost everything in trigonometry.
I had a candid assessment and told myself the truth. You can run but you will fail the exams. This exposed me to the foolishness of the approach I had adopted. This ostrich’s-head-in-the-sand tactics was a sure ticket to doom. I wanted to read Engineering. How does an Engineer hate maths or duck from one of its core concepts? Maybe I was going to be the first. Maybe. It seems I was equating myself to the doctor that hates to deal with people, tissues and organs. Or the businessman who does not like numbers.
It was one thing to know the consequences of my action or / and inaction. It was another to do something about the status quo. The issue at hand was that I need not love Sine, Cosine and Tangent. I need to understand them. What they meant and how I can use them as powerful tools to solve mathematical problems. Understanding first, love later.
Luckily, a new mathematics teacher, Mr Ijeoma, took over the reins of mathematics for my class. He was one of those teachers who love to teach. He had the afro hairstyle, of average height, walked with military precision though without the pomp. Further more, he was a disciplined and meticulous man. No-nonsense, spoke little but took his job seriously. I only heard him made one joke throughout but he was amiable and always available to help. With these characteristics, he took on trigonometry. He taught from first principles. He broke everything down to bare threads. He showed us what the threads that wove the dress, in a manner of speaking.
By the time he was done, I wonder what ever made me feel that trigonometry was a hard concept to comprehend. He simply made me look foolish. He practically showed me that I was running away from my shadow. To prove to myself that I understood the concept, I solved all the problems in the textbook and those in past examination questions. Guess what? I solved them correctly…all of them.
What I Learnt From Sine & Cosine
1. Mathematics is a language. Every language has its mechanics. If you understand the mechanics of how a sentence is constructed, you are bound to make good sentences with the right tenses. Eg he goes with his and him. He does not go with her. You get the drift.This applies to other things in life. Things are not arbitrary. If you take the time to put in the effort to understand, there is a likelihood, that you will follow proper order and get the required results.
2. Never ever think that you can wish away something you do not understand. This is wishful thinking and it leads to mistakes, failure and incompetence. If you cannot breath properly, then there is problem. you find a way to fix it. You do not wish it away.
3. For the fact that you do not understand a thing, does not mean that others do not understand it. If you think speaking Japanese is hard for an average Nigerian, please do know that there are many that can speak it fluently. Your job is to find them and learn the ropes from them.
4. There are always people ahead of you on any journey. Seek them and learn from them. This is where mentoring comes in. Get a mentor; learn from them and make fewer mistakes. Mr Ijeoma was always around. Why didn’t I ever go to him?
5. Understanding makes the journey easy. It smoothens things and enables you to manage your expectation.
In today’s world, understanding the next man seems to be a big sine and cosine. It seems like if the next man does not speak like us, look like us, grow up where we grew up, then he is an alien and hence does not deserve the right to breathe. It seems we want to be interesting rather than be genuinely interested to know more about the next man. If you are interested and invest some time into anything, like I did to sine and cosine, the secrets of that matter will be made known to you.
Taking the time to understand anything — people, a business, a theorem, a relationship — opens new vistas of opportunities for us. It helps us to know what our next move should be and the things to avoid as we move up the rungs of life. Taking time to understand breeds empathy and respect, a change of perspective and engenders mutual co-existence.
“When it comes to understanding others, we rarely tax our imaginations.”
― Lawrence Hill
What is your sine and cosine today?