I don't understand why I wasn't taught this in high school. They make the sine function look like wizardry when its actually really simple. Thank you for this video.
I've never seen a tutorial on the sine function before. I bet if I asked 1,000 people to explain it that 999 would fail. Another awesome tutorial that everyone should watch. Thank you!
Robert Hughes Excellent and thank you, tell your friends brother. If there is ever a question you have just leave it in the comments. I usually respond within 24 hours.
Man these visuals are huge. I remember all of the rules and ratios with all the trig functions but never really knew what they were saying how it related to circles or anything. Excellent!
First time in my life, I understood in real how the sine values are calculated. Till now I just crammed. This video was very very helpful in truly understanding the concept behind it. Thank you so much for such a nice explanation
1:04 so the hypotenuse is same for each of them. Denominator stays the same, and it's only the numerator that changes. The maximum value of the numerator can only be equal to the hypotenuse, never greater. Oh... this is beautiful, Saul!
I’m so glad I came across this video! It’s sad to think that schools only teach how to use this in a calculator without the students understanding a single thing of this simple concept.
I'm lucky to have access to videos like these at a young age (especially when I'm trying to re-learn the trigonometric functions to prepare for calculus next year). Thanks a lot for making this.
Thank you! I'm creating a folder labeled "need to know information" and I'm putting this video there. I've asked what is sine or what is the formula for sine and have never found (or heard) an explanation that could be visually represented like this! And now I believe I won't need to look up how to use sine, cosine, and tangent every time I want to find the opposite or adjacent when all I know are the degrees of angles and the hypotenuse. Whoop whoop!
Wow, that's fascinating, we've all been taught this by people that really doesn't understand, It is so much easier to learn by people that really understand the concept behind the theory.
Thanks for this explanation. This is a good background study for the student in order for them to visualize the use and function of the lines in the graph. I too got something from this clips...very nice, I like it.
I wish videos like this were around when I was in school. I took trig in high school and remember asking where these functions come from and my teacher looked at me like I was speaking another language. I hated math than but as an adult I find it eloquent and beautiful. Thanks for the awesome video
Excellent video; I think the big problem is that they teach us sin, cosine and tangent exclusively for acute angles (legs and hypotenuse of triangles); when in reality, it makes more sense to think of them in terms of verticals and horizontals; because, only in that way we will be able to comprenhend and calculate the trigonometric identities regardless of the size of the angle.
This is the first video of yours I have seen but "to hell with it", I am going to express my immediate reaction. You are like a god to me right this moment. Circles. Ha! If my academic results are any indication then I excelled in mathematics at school but, until this moment, I did not know that trigonometry had anything to do with circles. You believe that sh-t? I finished high school in 1993 and pretty much left all I knew to the side. Better late than never is my thinking on this one. Thank-you.
Excellent question, you may need to do some research on this but I am guessing it was either to build the pyramids or the greeks came up with it for their architectural structures.
I heard that some poeple were building a ship and they were cutting trees. When they needed that largest part in the middle, they haad to cut a tree of length the same or bigger than they needed so they could cut it off. They asked some mathematician if that tree on the hill was large enough for the last part. They wanted to know because if it was not large enough, they would have to find another and try it again. He came up with the idea of measuring length and angle of its shade in noon and make a 90° triangle out of it, where you had all angles (by subtracting from 180°).
Thank you so much. I completed my Diploma in Electrical Engineering. It was a simple wave that use in Electrical system. But i was ignore about sine wave mean where did it come from.
In high school, i used to be on one the best in my class but .... defining where it come and making me understand in 2:11 in the video its just.... i dont know ... magic
Hey! That's a pretty informative video. Although, I have a question on how you can consider a triangle to exist at sin(0)/sin(90) etc. Can anyone please explain?
I really appreciate your help. But I still don't understand how the calculator is given a value (for example 0.707), and it computes whatever trigonometrical function value the user wants. For example arcsin(0.707) = 44.99
In third quadrant we are using angle 210 degree which is outside the the triangle even though we are are perpendicular /hypotenuse for sin210 ,why? This is confusing
This is unironically helpful and all, but how did they figure out the angle out of just the height and hypotenuse??? Thats the real sorcery, how is THAT figured out???
but why did you make the radius of the circle 12" when you could have made a unit circle so the hypotenuse is 1 so the opposite of the triangle is sin(θ) and the adjacent would be cos(θ)
I used a radius of 12" because it was a 12" ruler that I used for the measurements. The video was done in such a way to give the viewer an intuitive feel for the ratios involved.
Hi boss. Great explanation.I am new to mathematics & i have a one question. What if we increase the radius from 12 to 20? will sin(30) always return 0.5? if yes, please elaborate how? As per my understanding. if we change the radius then on angle 30, height will be different to get 0.5. is it?
yes, sin(30) will always be 0.5. If you increase 12 to 20 then the hight will be 10 and the ratio will be 10/20=0.5. The ratio of the opposite to the hypotenuse is always the same. Hope this helps.
It's how the sine function is defined. For a given angle, you find the height of the triangle and divide by the hypotenuse, and this ratio is always the same for any angle. That's why the sine function is so useful, because you can use the ratio to find other sides of the triangle. It's useful in construction and so forth. Here's a video that explains why it's so useful: ua-cam.com/video/NSzPWOn_LfQ/v-deo.html Hope this helps. Feel free to ask your question again in a different way if you need. Even though these videos were made some time ago, I still reply to the comments when students are having trouble if the video isn't clear enough.
I don't understand why I wasn't taught this in high school. They make the sine function look like wizardry when its actually really simple. Thank you for this video.
so true!
I'm 34 and now I learned where it came from.
Agreed!
I'm just seeing this. Thanks for your kind words. Yes it really is much simpler than I was taught in high school also.
Because high school teachers most likely aren't as competent as university professors. They learned it and just parrot it back to you.
I've never seen a tutorial on the sine function before. I bet if I asked 1,000 people to explain it that 999 would fail. Another awesome tutorial that everyone should watch. Thank you!
This is brilliant, i've searched a few different videos for a good, thorough explanation and this is by far the best i've seen. Well done!
Robert Hughes Excellent and thank you, tell your friends brother. If there is ever a question you have just leave it in the comments. I usually respond within 24 hours.
I am from India.Usually Indians don't teach like this.Great sir.Hats off
Poda isuku
Man these visuals are huge. I remember all of the rules and ratios with all the trig functions but never really knew what they were saying how it related to circles or anything. Excellent!
Yes - I was fifty years old before I discovered Newton’s statement to the effect that almost all of maths was contained in quarter of a circle.
First time in my life, I understood in real how the sine values are calculated. Till now I just crammed. This video was very very helpful in truly understanding the concept behind it. Thank you so much for such a nice explanation
This is the best explanation of where the sine comes from that I've ever seen. Great job and thanks a lot!!!
After 6 years of high school I finally understand how it actually works. Thank you good sir!
1:04 so the hypotenuse is same for each of them.
Denominator stays the same, and it's only the numerator that changes.
The maximum value of the numerator can only be equal to the hypotenuse, never greater.
Oh... this is beautiful, Saul!
correct. and for a given angle the ratio is always the same. even if it's a larger triangle, the ratio of the two sides will be the same.
I’m so glad I came across this video! It’s sad to think that schools only teach how to use this in a calculator without the students understanding a single thing of this simple concept.
What a clear and simple explanation, thank you ! I really wish I had high school math teachers like you.
As a first year engineering student studying ac circuits for the first time, I find this one very helpful. You are a life saver!
This is the one video I didn't know that I needed. Thank you so much, Sir, you are a life-saver.
Absolutely brilliant. A logical, simple demystification of the function. Should be taught this way in school.
That seems, to me, to be the most thorough way to explain the mathematics of sine waves.
I'm lucky to have access to videos like these at a young age (especially when I'm trying to re-learn the trigonometric functions to prepare for calculus next year). Thanks a lot for making this.
The best explanation I have heard so far. Thank you sir.
Thank you!
I'm creating a folder labeled "need to know information" and I'm putting this video there. I've asked what is sine or what is the formula for sine and have never found (or heard) an explanation that could be visually represented like this!
And now I believe I won't need to look up how to use sine, cosine, and tangent every time I want to find the opposite or adjacent when all I know are the degrees of angles and the hypotenuse. Whoop whoop!
Sine of theta = position of curvature relative to its radius.
Thank you! I was looking for understanding on this!
Best Damn Trigonometry tutor by far!
I just realized that I had no idea what sine actually was and I just used it without thinking. This makes a lot more sense now
Wow, that's fascinating, we've all been taught this by people that really doesn't understand, It is so much easier to learn by people that really understand the concept behind the theory.
amazing!!!!!!!! so easy to understand !!!! your teaching is so interesting. thank you !!!!!!!!!
Lo and behold!
Thanks for the vid
Went to the comment section just to see if someone mentioned his repeated use of "Lo and behold" LOL!!!
@@ncasey9519 Lo and behold, I did too!
Much Thanks from india
Thanks for this explanation. This is a good background study for the student in order for them to visualize the use and function of the lines in the graph. I too got something from this clips...very nice, I like it.
I got my answer, searching for 4 years. Thank you.
I wish videos like this were around when I was in school. I took trig in high school and remember asking where these functions come from and my teacher looked at me like I was speaking another language. I hated math than but as an adult I find it eloquent and beautiful. Thanks for the awesome video
And I just noticed this video was posted in 2011... the year I graduated. Maybe I just didn't care haha
Thanks for the props Andrew!
Amazing explanation! Now i finally understand how the functions actually work
This is a great explanation
This is amazing! I have been looking for an explanation on the correlation between the Sine function and the unit circle and this is it!
Sir this is beautiful. Thank you so much for this explanation by forming a Sine wave with it too
This is what I was searching from long time..great explaination..
Bravo! You made this interesting!! If only college math had been so. We certainly hope you are a professor somewhere! Best of luck!
Awesome explaination... He deserve googol googol likes.
Excellent video; I think the big problem is that they teach us sin, cosine and tangent exclusively for acute angles (legs and hypotenuse of triangles); when in reality, it makes more sense to think of them in terms of verticals and horizontals; because, only in that way we will be able to comprenhend and calculate the trigonometric identities regardless of the size of the angle.
I'm surprised this brilliant video has got so little views
What an amazing explanation , I'm an engineering student , but i don't knew it as clear..
Thank you :-)
A huge big thank you for this excellent exploration.
It really helped me a lot.
Thank you sir!
You are a wonderful teacher!
This is the first video of yours I have seen but "to hell with it", I am going to express my immediate reaction. You are like a god to me right this moment. Circles. Ha! If my academic results are any indication then I excelled in mathematics at school but, until this moment, I did not know that trigonometry had anything to do with circles. You believe that sh-t? I finished high school in 1993 and pretty much left all I knew to the side. Better late than never is my thinking on this one. Thank-you.
Good explanation.Easily understood
Very clearly explained. I got a great lesson.Thank you very much
Great - simple clear and concise.
Thank you sir,my doubt is completely cleared
Wonderful video sirr😊😊😊😊
What a great way to explain the sine function!
I thought so too! Share with friends!
Thank you sir...its really a nice explaination..i got very useful points from this lecture
This should be mandatory in all math classes
Thank you very very much! It was a very helpful explanation!
Thanks gods. This was killing me for years. I understood the maths but not why it is.
Very nice sir, God bless you
Thanks. Now I understand it clearly
why it was invented & what was its application in the very beginning?
Excellent question, you may need to do some research on this but I am guessing it was either to build the pyramids or the greeks came up with it for their architectural structures.
thanx Sir
I heard that some poeple were building a ship and they were cutting trees. When they needed that largest part in the middle, they haad to cut a tree of length the same or bigger than they needed so they could cut it off. They asked some mathematician if that tree on the hill was large enough for the last part. They wanted to know because if it was not large enough, they would have to find another and try it again. He came up with the idea of measuring length and angle of its shade in noon and make a 90° triangle out of it, where you had all angles (by subtracting from 180°).
i heard that a mathematician first discovered it for the love of math itself and he knew no applicable use case for it
EXACTLY the reason i googled it today to know what it meant and reason for invention
I would argue that this is how to use the unit circle. I was trying to find more information on the series.
Thank you so much. I completed my Diploma in Electrical Engineering. It was a simple wave that use in Electrical system. But i was ignore about sine wave mean where did it come from.
Thank you, Sir, from my heart.
In high school, i used to be on one the best in my class but .... defining where it come and making me understand in 2:11 in the video its just.... i dont know ... magic
why taking a circle and a triangle ? what is the applications of that ?
Thank you for this quality video
Hey! That's a pretty informative video. Although, I have a question on how you can consider a triangle to exist at sin(0)/sin(90) etc. Can anyone please explain?
thank you so much this cause problem for me at finally I got a solution with your help.
Amazing discription.. 👌👌
Beautifully simple!
How did you draw the 12 inches circle precisely and plot the graph on the whiteboard?????
So cool
I used a 12” ruler. For the circle, I used a magnet in the center and some zip ties to trace the circle. Cheers.
very nice bro
Great explanation thank you
Thanku sir, I got understood very well. Keep making viedo and keep things easy. 😊
great explanation. thanks a lot!
Best Explanation !
but why draw a triangle within a circle? what's the use case for it?
Well explained Thankyou.
but how does it work internally? you can't measure the side and get a high precision
Great presentation but I wish you would have used the hypotenuse of 1 like web are learning in the textbooks
Great explanation for sine function
Thank you Sir for your good work
Thank you
Thanks very much,man..Thanks a lot again..
Thank you! I learned something.
this is great. I have had tried to search for video with similar info like this one and I couldn't.....
then UA-cam Brough me here 😂
I really appreciate your help. But I still don't understand how the calculator is given
a value (for example 0.707), and it computes whatever trigonometrical function value the user wants. For example arcsin(0.707) = 44.99
I think it has something to do with Taylor series approximations. You should look it up.
Aman Deep , that sounds promising!
Cos(45°)= sqrt2/2= 0.707....
FFFFFFF School...
These teachers are horrible.
This is so clear and simple.
Hey..so we as light beings exist in the fragmented existence of sinE waves?
this is cool and all but what does the sine represent and why does it exist
Thank you sir, well explained
I still dont understand why sin works? Is it just a matter of fact? like pi?
I wish my teacher would have taught us this way 😍
That was interesting. Thank you!
Brilliant🤔😁😃
good explanation
In third quadrant we are using angle 210 degree which is outside the the triangle even though we are are perpendicular /hypotenuse for sin210 ,why?
This is confusing
At 210 degrees, it's a triangle that has a negative y-value (-6/12)= -0.5. You can think of each triangle as separate triangles.
This is unironically helpful and all, but how did they figure out the angle out of just the height and hypotenuse???
Thats the real sorcery, how is THAT figured out???
Holy shit...this actually made sense for me. And I'm as dumb as they come!
great explanation. thanx a lot. what is the name of teacher?
but why did you make the radius of the circle 12" when you could have made a unit circle so the hypotenuse is 1 so the opposite of the triangle is sin(θ) and the adjacent would be cos(θ)
I used a radius of 12" because it was a 12" ruler that I used for the measurements. The video was done in such a way to give the viewer an intuitive feel for the ratios involved.
Hi I like your video
I looked and I beheld, thank you
Hi boss. Great explanation.I am new to mathematics & i have a one question. What if we increase the radius from 12 to 20? will sin(30) always return 0.5? if yes, please elaborate how? As per my understanding. if we change the radius then on angle 30, height will be different to get 0.5. is it?
yes, sin(30) will always be 0.5. If you increase 12 to 20 then the hight will be 10 and the ratio will be 10/20=0.5. The ratio of the opposite to the hypotenuse is always the same. Hope this helps.
@@saulremi Thank you so much.
@@sanihyne7751 you are most welcome. Share with your friends to pay us back! :)
How sin¢=y/R comes because you are taking sinx as height divided by hypotenuse . Could u please tell me how this is formulated
It's how the sine function is defined. For a given angle, you find the height of the triangle and divide by the hypotenuse, and this ratio is always the same for any angle. That's why the sine function is so useful, because you can use the ratio to find other sides of the triangle. It's useful in construction and so forth. Here's a video that explains why it's so useful: ua-cam.com/video/NSzPWOn_LfQ/v-deo.html
Hope this helps. Feel free to ask your question again in a different way if you need. Even though these videos were made some time ago, I still reply to the comments when students are having trouble if the video isn't clear enough.
honesstly, it is today that i understand and know the origin of sine function.
Excellent compliment. Thanks for your kind words.
@@saulremiRémi you are welcome my Teacher. I'll be back for more...
@@ikpeessien7399 share with your friends brother. where are you btw?