Where do Sin, Cos and Tan Actually Come From - Origins of Trigonometry - Part 1
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This video looks to seek where Sin (Sine), Cos and Tan actually come from.
Looking at the ratios of the sides of right angle triangles, we can notice certain patterns if we measure different right angle triangles with the same angles. Very similar to how ratios exist in circles with circumference and diameter to discover Pi.
We can then make trig (trigonometry) tables for all the angles and then draw the graph of sin(x) which forms the sine wave.
These trig ratios help us finding missing angles or sides in triangles by using SOHCAHTOA (SOH CAH TOA).
The sine function can be obtained by taking ratios of triangle sides at different angles.
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Thank you for watching.
The key to why this video is so good… You walked through the narrative of discovery. This is what so many mathematics teachers do not understand if they taught math like history, then it would be better understood by most.
I was going to to say exactly the same thing. But only the best of teachers who know and love to understand mathematics teach this. Unfortunately nowadays it's just superficial teaching just to get the marks.
I had Trig in high school, then a review in college. Both times, I struggled with the Trig Identities, because we were supposed to memorize them. Years later, I wanted to go back and take my math studies further. I took Trig as a refresher and the Professor introduced the unit circle. I immediately realized that what I'd been struggling to memorize was nothing more than the Pythagorean Theorem. They had just renamed A, B, and C as Trig functions. Why didn't anyone else explain that?
Indeed. -All maths- _Everything_ should be taught with context, not just rote memorization.
Same here, teachers and lecturers never provide the basic foundation.
That's why i hated maths when I was in high school.Most teachers don't go deep into the subject and dive through an explanatory of why we using those principles and why it's that way. I'm that kind of person who needs to understand the essence of the matter in order for the bulb to light up and having those 'aha' moments. At that point,it would be a lot more smooth and would make more sense for us. We are so priviledge to have internet nowadays and be able to catch up all of that.
I am a 66 years old person , I wish some one told this then . It is so simple however the way we were taught we never understood what you explained .
Now I will teach my grandchildren through this vedio .
Well done my boy May god bless you
The great mystery is solved! I am 62 and finally seen the light.
I am 58 years, I had to take biological science because non of my teachers in school taught this secret but had to mugup the formula not knowing the secret. Good job !!
Same here
@@powerwagon3731 Me too at 70 yrs old and I finally see the light!! Why wasn't this the very FIRST thing taught to us in trig class in school!
im 99 and damn this vid changed my life
2 years no part 2
Like for real even with another account ,maybe
😢
it's insane how schools seemingly don't teach like this to be time efficient but completely fail to realize it's the things like these that add a sense of discovery and engages the student far more efficiently than simply memorizing the soh cah toa rule for the sake of a grade which at those ages one could simply not care for specially if you're from a lower class non academic family.
Istg last time i asked my teacher on how is cos60 equal to 1?? she said just put it in the calculator it really saddened me
....but don't worry, there is plenty of time spent teaching stupid "pronouns" and why boys can use the girl's bathrooms.
tbh it's because most teachers(at least outside of a college level/public schools) probably didn't even know about this and are just taught to teach certain concepts.
It is sad to think about the past when we didn't have the Library of Alexandria in our pockets and you were forced to learn from people who barely understood math and gave inaccurate or no explanation behind their reasoning except "we're adults".
bro left us on a cliff hanger for 8 months now💀
Over a year now, maybe the maths hasn't been invented yet? Hahaha
@@Rdkubala maybe?
@@standowner6979 uh bro this is just basic trigonometry there's way more advanced maths they teach us 😭😭😭
@@prakharmishra5583 I know some people don't get sarcasm, but dang! It's still annoying when it happens to you.
I know about Real Analysis, Groups, Rings, Fields, Galois Theory, Ergodic Dynamical systems, etc.
@@standowner6979 ah nvm happens with everyone, have a good one
After thirty years, this is the first time that I finally understand WTF are sin and cos.
This is so weird, in order to understand something as simple as this, we have to waste many years of struggling.
I really appreciate what you've done 🙏♥
How were many years wasted?
I've come to the same realization. How could I have not understood this???
This should be the first lecture when teaching Sin, Cos, Tan... but I think even the teachers don't know about this.
It wasn't you; it was your math teachers, who took a simple subject and made it incomprehensible, by teaching math as if you already understood it, with no explanation of the underlying principles, relationships, or purpose in learning the math.
Even Carl Sagan, the famous astrophysicist, said that when he was young, math teachers taught purely by rote, with no explanations or understanding themselves what they were teaching.
@@number5322 , Because your teachers made it incomprehensible with their teaching methods. When I was a kid, students learned In Spite of their teachers, not because of them.
When you find out you failed trigonometry because your "teacher" had knowledge but completely lacked understanding...30 years later
I would love more teachers telling why this kind of stuff works and why it's useful instead of just teaching you how to do it, it turns it from daunting to actually interesting
It helped me that I was coding and experimenting with these functions. Loop from 0 to some random number, put sin on the x axis, cos on the y and hey look, it's drawing circles! Cool, but no idea what I could do with it. It later made sense that it could be used to move a character on the screen in a certain direction and speed.
Fast forward 3 decades, there are probably a lot of libraries that take the work of making game physics out of your hands :)
Thats why im glad my math teacher shows how all the stuff we learn is derived. although we're not at trig yet.
5/8/2024 - The utility, I.e., usefulness, of trig is learned through word problems, studying calculus, physics, navigation, chemistry and electric circuits.
Unironically the best explanation I’ve seen. Now judging by his posting schedule we’ll have part 2 in the next month or so
😂 right!
Guess again. Its a shame, the first one was good. Gonna gave to look elsewhere for the conclusion.
Seven months later…
@@roundhouse2616 oof
After 1 year........
I wish conceptual explanations like this were given in school. I was good at maths but this would have given me a much better basis
same
You were... but you weren't listening.
same with me as well
@@billdavies6463 speak for yourself
@@billdavies6463 nah i never knew the actual value of things like rad3/2, but knowing its just.866 is mindblowing
I was an A maths student right up until Year 9. The last thing I remember encountering in maths was SOH CAH TOA.
I never understood it (or the strong accent of my teacher), and it was never explained to me in a way that made sense. I fell behind, started failing, and dropped out of school after Year 11.
I'm 48 now, and you just explained Sin, Cos, and Tan in a way that I actually understand!
Thank you. 😀
Excellent video, I haven't done any trigonometry is over 20 years and found myself trying to wrap my head around what a sine wave was. This video was perfect. Thank you. Please do more.
It’s been over a year, and I’m still waiting for a part two. There’s no other video that explains it as well as this one. Surprised there’s so little views…
by far the best explanation of Sin, Cos and Tan i've ever heard
That you explain it from the ground up instead of the normal "it's just a rule, learn it" approach makes it so much easier to understand....almost seem simpel now
In Vietnam, we learn the formula via a poem:
"Tìm sin lấy đối chia huyền
Cosin lấy cạnh kề, huyền chia nhau
Còn tang ta hãy tính sau
Đối trên, kề dưới chia nhau ra liền
Cotang ngược lại với tang."
It's nice to see many adults come here to check their memory like I do. Love the way you guys remember it: SOHCAHTOA : easy peasy :)
I've been through maths half way thru calculus and this is the first video I've seen that has illustrated this concept so succinctly.
Regarding 6:58 Trigonometric Table. Before the invention of the electronic calculator, the logarithmic Slide Rule was a handheld calculator commonly used. A Slide Rule having trigonometric scales could calculate Sin, Cos and Tan. The S Scale was used for Sin and Cos. The T Scale was used for Tan. The ST Scale was used for Sin, Cos and Tan for angles less than 5.74 degrees.
I remember slide rules, but never got to use 1 because by the time I got to take basic geometry in junior high, trig tables were the order of the day & by the time I got to take elementary functions in high school, calculators were.
How could I know about slide rules if I never used 1? They were incorporated into the pen & pencil boxes one used to buy for school back in the 80's & earlier.
Paused at 3.32 to just sit here in disgust remembering my college trig encounter. But, I discovered from that same era, it's the presentation that makes all the difference. So, thanks! The best presentation of this material I've seen on CZcams, without question.
Ever since a teacher (20+ years ago) told the class that the code in computers and calculators to calculate Sin is several pages long, I've though Sin is some impossible thing for me to ever be able to understand, so I have avoided sin/cos/tan as much as possible when programming (as I prefer if my code relies on things I understand). But now, youtube recomended this video and I thought I could at least give 10 minutes of my life to try and see what Sin is all about.... and yeah, wow, that was simple to understand. Thank you for a very elegant explanation. :)
Calculators, especially 2 decades ago, used numerical method to calculate Trig values. For Sin would be Angle-Ang^3/3!+.... so..even though several pages might be exaggeration, your teacher was in theory correct.
@@wasay456 In fact 30-40 years ago if you needed a fast SIN or COS function what you used was a precomputed table of values so it may not be an exaggeration...
This video is awesome, because it most importantly explains WHY these functions exist.
Not like in school where the teacher just blabers out the equations & goes about his/her day.
Understand it. Unfortunately 55 years after taking my school maths exam.
I learned this about 50 years ago... I understood it well then but I wish there were teachers like this in the old days. Trigonometry and Logarithm tables used to confound me as to their purpose in life! Well done Mr. Syed.
OH yeah, how is the log derived? That was also on my mind in college algebra besides how sin and cos are.
Because you are not meant to learn it, they just want you to memorize everything and perform to each test which is not a good way to understand the topic but just making people go through a class to class
@@RPSchonherr
One Scottish mathematician had a brilliant breakthrough before calculus was an understood concept according to Wikipedia. Look up history of logarithms page there,. "Napier conceived the logarithms as the relationship between two particles moving along a line, one at a constant speed and the other at a speed proportional to its distance from a fixed endpoint." Dude literally just... went "logarithms!" and it caught on.
My father had only the 4th grade (b. 1944) and started working with 10yo as tinsmith apprentice in is uncle shop. He told me that he found the relationship (pi) between diameter and perimeter to help him cutting the metal sheet with proper dimensions.
I am 1005 agreement with you and I am 77 and from India. During my grade 11 & 12 the Math was a nightmare, but because of the family and social pressure I somehow managed to score well to make it to a good Engineering college. But again transferred from Electrical to Metallurgical engineering because of high math required in Electrical. Later when I settled in life, I started a second look at regretted that I did not have good teacher. not only Math, other topics too I try to refresh using internet. Wish we had something like that in 1960s.
holy hell this channel is a goldmine, I wondered where these random numbers came from, I sort of just mechanically did the formulas my teacher told us. Thank you!
BRO R U REALY A VIRIFIED GAMER
When a gamer learns trigonometry. RESPECT TOWARDS TRIGNOMETRY+++++++
noice
nice to see you here !
Trust in Jesus Christ LORD and SAVIOR Amen
Reminds me of Mathematics in high school in South Africa in the late 60s. Each of us had what we called a "log book", which contained all the values of sine, cosine and tan, as well as all the logarithmic tables (no calculators then!).
Honestly, when you know the purpose of all these maths it helps you learn it more quickly and efficiently. That's why I searched for it and I am glad I did.
I'm two years late, But I have to congratulate you on teaching mathematics the way it should have been taught, through logical discovery and abstraction. Mathmatics is a tool, a utility, and using it as such helps with understanding it.
Sir, I just sub'd.
I wish I'd had you as my math teacher in High School when I began studying trigonometry & algebra.
You're detail & I sights clarifies a great deal...and so easy to understand.
I'm 68 years old and retired now.
You actually make this instruction....fun!
Wow! I was really good at maths but missed a year. When I rejoined after a year in college and trigonometry was rushed through, I was clueless. I wondered what the heck Sin, Cos and Tan were. Now I understand... finally.
I wish I had this visual aid in school, our teachers made it hard for us to learn anything, as if they enjoyed seeing students struggle. This was in the 90's.
Seriously, this is why most students struggle math. Teachers should take note how this was explained and it has more sense. In my days, my teacher will just jump on something and don't bother to explain why it's like that, just deal with it. So you end up memorizing it and doesn't have any importance and eventually forgot about it.
Please do part 2! I'm struggling with trygonometric functions and this is the first video that makes me sense about this. 🙏🙏
Hey it has been 5 months since he has uploaded this video do you know where to find part 2 if he uploaded it
@@amrwael4261 lol it's been a year now
@@aurapain5757 still 🤐
@@muhammedzaid857 still waiting
Still waiting 🍺
Reading some of the comments here, I can only wonder what kind of teaching actually goes on in school these days. What was shown in this video was exactly what was taught by my math teachers. I remember being shown the unit circle & how all the sin, cos, tan, & their inverse angle values were derived from it. Logarithms & natural logarithms were the things I didn't fully grasp: just enough to mechanically solve the problems, but not enough to fully understand what I was actually doing.
I'm so old, calculators only became affordable when I was in my 2nd or 3rd year of high school. For the first year or two we had books of printed tables of Sine, Cos and Tan values. I still remember the mnemonc See Old Harry Come Along Here To Offer Advice.
Being a maths teacher is a gift so few of them around it is such a beautifull thing once you understand the basics
This was never spelled out as I recall, in school. Where as others have said, they learn more from you tube than school. Where knowing how to teach is an actual skill. Knowing the subject is a skill. Thoroughly knowing the subject and demonstrating application gives it rational meaning so one knows what they be doing.
Miss Pietsu was an excellent math teacher I had, but she wasn't with public school system.
I am 70 next birthday, I have never had this explained, not at school or work. I got by by always following a predetermined method
You made the helpful simple assumption that the person does not know what youre talking about, and started there
I hope you return
Thanks
I switched off from my studies as a young student because no teacher could explain the relationship between the Sin 0.5 and Cosine 0.866 values, etc. They were too busy wrapped up in numbers without any visual clues.
If only my teacher had drawn a circle on the blackboard and split it into quadrants. Forming the x and y axis, and then said, treat the radius as one unit. Project an angle ( let's say 30° through the centre of the quadrant) and where it meets the circumference (1 unit= let's say 100mm for the purpose of the exercise), drop a perpendicular intersection to the x axis. That would be 86mm (0.86).Then, project a perpendicular intersection to the y axis from the same point on the circumference, which would form the 50mm (0.5). Therefore, forming the relationships between sine and cosine. And Tan would be the intersection of the y axis, hence the reason it's infinity at 90°. It would have made so much more sense earlier on in my life. After that, it's all simple ratio and proportion, which you've explained really well here.
Hands down the best explanation for something that I was asking about in grade 10 many years ago....no one ever could explain it to me while I was in school. They just told me to use the Sin/Cos/Tan function without explaining what they were for. I am not sure if there is a place for this in every day life...but I am sure if I thought about it long enough, I could find a way to use it every day.
Sin/Cos/Tan is VERY helpful in finding a point on a circles edge when you know the xy coordinates. But this video shows the graphic representation of these ideas. Once you understand something visually it is hard to forget it. He did a good job here. I am an automotive technology instructor and I have a goal in my class, , or motto if you will, of NOT teaching people what I know, rather to tell them what they NEED to know, to understand the subject matter. Believe me, the approach make a difference.
Darrow...for the Prosecution
Thats how other people who truly understand mathematics are able to innovate and build amazing software like 3d design programs, or create vector databases and come up with all these similarity search algorithms. If all math was taught like this, most people will be really innovative with it. I'm still to understand what exactly integration does in real life lol
Thank you. That was clear and concise even to me, a musician. I vaguely remember it was a way of finding the height of a lamp post without having to climb up it and dangle a tape measure. In my day, pocket calculators hadn't been invented so we had pocket sized books of these three tables instead!
Amazing! After using these functions for years, I was finally like: What the hell am I actually doing? This really cleared my questions - thanks!
And I always ask myself where did the Pi come from and what is the relation between the triangle and circle, this presentation gives really an awesome explanation, thanks dude.
Great work sir ! .. I wish school teachers had same simple approach. My Love for maths has grown over the time but lack of basic always pushed me back.
I am 34 now & I feel this is the first time I could actually understand the entire narrative of Trigonometry . Thx a ton brother
After 50 yrs, I again learned about trigonometry thanks a bunch
You have taught basics so well, very beautifully explained, nobody taught the basics this way
yes, it is true that someone else came up with that theorem first, but you brought to clarity for at least myself. Thank you!
in my 27 years of age and collage highschool and elementary NO ONE HAS EVER PRESENTED IT BETTER THAN THIS
If it was i would had long finished collage by now and not be dropout...
Superb explanation. I wish schools and textbooks should also explain like this. Great Work.
Thank you.
When I was studying math (all those eons ago), they taught to the exam, it was enough that when given the question we could (most of the time) calculate the correct answer. Our teacher never really explained why. (Perhaps she didn’t know why herself 😱)
Back when I was in junior high school in the early 1990s, I got really into computers and coding. I was playing with making graphical programs that would display things, like flying through a starfield and stuff. I knew all the geometry stuff about triangles, and realized that the ratios of different sides and angles would hold for right triangles, and made code to let me create pseudo-3D stuff (like you would set a point in 3D, but it would figure out what 2D location to actually put it on the screen through using these ratios to figure out all the lengths needed). The next year in school we had trigonometry and I discovered all these ratios I had been using had names like sine, cosine, tangent. I always wondered why in class they never really explained it based on the ratios that become obvious once you've had geometry and learned about similar triangles. It seemed very intuitive that way for me.
This is the one thing my school failed to explain but now makes things so much easier.
so far the best video on understanding the primary knowledge about trig. keep up the good work.. i hope part 2 is coming soon
Your the man i am searching all over in CZcams,your doing great job in mathematics and i am waiting eagerly for your videos
BRO, UNDERSTOOD EVERYTHING. I was paying a lot of money for instructor cuz Im struggling with math for final exam, especially angles and trigonometrics. Thank you
I used to hate Maths in school. I used to feel less capable but as an adult, I realise all my teachers sucked. I wish I had a teacher who would explain maths this well, my grades would have been great but I won't regret
This video was really well made and you're very talented at explaining these topics, I'm looking forward to a part 2
Part 2 please! Such a good explanation!
Well done ,not some high school know it all .
I cannot express how grateful I am for this video. Incredibly consice and informative. Im studying engineering and I seriously needed this, as I now COMPREHEND trig functions, thanks to your clear explanation. I hope you continue uploading. Again, thank you
Jesus Christ, I’m in *college* and this is the very first time anyone has ever explained this to me in this way.
Seriously I’ve gone my whole academic life without ever connecting the actual understanding between Sohcahtoa and the universal outputs they’ll create
2 years still no part 2 😞
This is for the better …
I found part 1 to be mediocre and poorly made enough.
So sin is an operator which converts the angle in a right angle triangle to the ratio of the opposite side and the hypotonese side. Brilliant
Excellent. This is the first time I've ever understood where sine and cosine come from, and what they mean. Thank you!!!
This is the best explanation of the basic trig. functions I have seen. Like many other commenters on here, I wish to God I had seen something like this when I was a kid; I would have been much less afraid to take trigonometry and other math courses, which I aways assumed I would fail (and would have failed, given the horrible math teachers I had, which taught purely by rote, with no explanation of relationships or purpose in the math).
so after 28 years, the concept is again restored, Many thanks Syed.
Never had use of them, but now actually understand what they are. Excellent presentation. Thank you.
34 year old man in college learning to do IT maths and coding HTML and my lord maths somebody kill me now but im getting there and your videos are an amazing help to me
such a good vid ❤️
Looking forward to the next episode
I wish I had you 12 years ago when I was in 10th studying trigonometry for the first time..
Bro, if I had found your explanation a while ago I would've stay in school. Good job
This was amazing, please make a part 2 ! I would absolutely love it to have the next part of the story !
guy probably ded
love it, really the basic concept "all you need" that introduce Trigonometry
this is amazing to see how necessary this post is from time of post to present and people begging for more..I used trig to cut wood frames with precise dimensions..this video is fantastic
If online resources like this was available during my days, I think many students could have landed on a better career path.
I wanted to be an ECE during my days because I was so curious how electronic things work, but due to my poor math skills I never pursued it.
It is fascinating nowadays how information / knowledge is very much accessible for almost everyone but very unfortunate that many students nowadays do not grab this kind of opportunity to learn things.
thank you so much , I had a hard time looking for an amazing and simple and procedural explanation such as this one , you are a life savior.
Love the explanation. Congrats. Suddenly noticed at 7.51, the wider angle in right-angled-triangle after 90, is 60. But the picture depicts shorter angle with 60. The picture should be corrected with length.
It’s been 20 years, now I understand it. I don’t blame my teacher completely, I was just a teenager and i didn’t really care but if it was taught the way you did may be it would have made it easier and sparked some interest.. anyways now I’m an artist 😊
Wish they'd taught me this in school ... It's logical and easy to follow. At school in UK back in 1960s, they dived right into the algebra without this basic stuff.
I would be really surprised if they didn't teach you this in a way that was very similar to this. The problem is this would have only been 1 tiny 10 minute portion of a larger course, so you probably either weren't paying attention for those 10 minutes and/or forgot about it.
Great video. I found the knowledge discovery teaching method sooo valuable. Thanks!
I was taught this 45 years ago!
Glad I remembered it right (well done Mr Bohana ... a great Math teacher Chess instructor and Olympic Judo contestant)!
in my senior high school, I solved a trigonometry problem and at the end the teacher asked me: what is a cos? I looked at him with a blank expression; thinking "I just used it, but I can't explain what it is". 20 years later, now I can explain it 😆🤣🤣
Bro took longer time to release part 2 than avengers end game
Been watching this type of tutorials for a while, and just now, i realized that none of my professors back in high school and college ever relate these things to actual stuff in real world. That these topics are derived and developed by resolving problems in real life. I wished someone taught me math this way.
Why they didn't teach us like this in school? I hated trigonometry, now I love it. Thanks bro, you're the best.
Lo l - said in a polite way - the changes in your tone really do tell where you get confused / excited by how maths might explain or show something yet to be seen in life
Thank you. You've taught me more in the length of this video than I ever learnt at school.
you "learnt" in school?? You need to go back.
"Ever"? Seems a bit of an exaggeration. You learnt proper punctuation and capitalisation. But really, you either attended school for less than 9m 14s, or you suffer from severe retrograde amnesia. Or you are exaggerating...
*2 YEARS ?!?!!!*
This is the way teach students those who are studying trignometry , a big salute
I appreciate your teaching style !
Without doubt I would have been an accomplished engineer had I been taught practically like this. I simply couldn’t comprehend and ended up just scoring 80% and moved on without entering engineering subjects. I can’t marry something without knowing its fundamentals. Somehow I had to byheart with a heavy heart. Amazing video
Honestly they never taught this in school 😭 thank you so much 😀
Just the the explanation I needed to hear.Thank you man
After so many years of my life Today only I noticed how the Clark's table was prepared for all the angles 0 to 90 Very good teaching Hatts of your knowledge
I've struggled with this for so long and you just explained it in a surprisingly simple way. You should be my teacher like fr.
Great video, brother. Keep up your great work. It will help a lot of people.
Bruhh wheres the part 2. Its been 5 monthss
TWO years now :-(
This is amazing. Where has this this video been my whole life?