That proof of how the points break the arc length into thirds is what I was searching for! You came so close to saying it then didn't!! Wonderful video nonetheless. There is some rare knowledge in it. Thank you.
Trigonomic Functions decoded.. Wow! Very impressed with the way you have taken out all the complexity from the functions, and reduced them into simple concepts that one is able to understand. You really turned our light Bulbs on!! That was powerfull!! Thanks a million for the video !!!
I have been looking for a explication like this for more than 16 years. 16 years! so thanks! finally a answer to wtf Sin and cos is, that did not just leave me more confused.
Often trig is taught as part of algebra, but it can also be taught as a separate course after the first algebra course; it really depends on how your instructors choose to teach it. It could be taught in a class called Algebra II, for example. Certainly trig is always taught before calculus, since trig is used and discussed in detail in all calculus courses. In summary: trig usually appears after the first algebra class but before calculus; exactly where depends on your curriculum.
The easy way to produce the unit circle is to divide a circle into 24 equal 15 degree graduations. Number these points from zero Pi to 2 Pi 0,1,2,3... then take those numbers and multiply them by Pi/12. You will have 8 extra locations on the your unit circle that you can use or throw away. The same method can be used to give you any number of equal graduations that is an even number. Just change the denominator to half that number.
I wanna say that, this is just fantastic. I have to watch this video and also your other videos over and over again. Actually I'm a collegian and was here after searching "Trigonometry Application". I wanna know how trig will relate to electronics and specially signals and signal processing. By the way thanks for this very valuable stuff.
This is a brilliant video! Currently I am self-teaching myself maths for the ACT, and before doing this I had never encountered trigonometric functions and the unit circle. Completely confusing is how I would describe all of the other videos/revision websites I have watched/read (in the case of videos in particular, because they fail to allow enough time to properly explain what's going on! This video, on the other hand, goes the full thousand miles!). Thank you!
Agree. Khan academy has much more videos about more topics in science, and this channel has increidible awesome attention to detail. Both combined are great tools for learning.
Maybe someone already mentioned it but the trig identities listed at 36:32 have the x,y value backwards for sin/cos 30 degs. Sin (y) should be 1/2 and cos (x) sqrt3/2. Not a nit pick, just good of the order. Great video!
I did not understand these terms in my life as I understood from this video, I lift my hat respecting for you and for your style in the magnificent explanation
Really, Khan Academy is a wonderful school of knowledge because I learnt from it what my teacher a week or more than within minutes that is amazing thing!
I found this very interesting because at the 41:36 I can assimilate the waveform of sine as AC generator in circuits, same as cosine, and the Tangent looks like the inductor wave on the oscilloscope, now everything makes sense for me, even though the purpose of this vid wasn't similar of what I discovered, I'm thankful that I have clearance on where those things came from. Thanks, sir.
Thank you SO much for posting this video!! I was looking at this like it was a foreign language before I watched it! It was very hard to find a video that did so a great job of explaining it!!
Why trigonometry tables are never mentioned? In the 1960s, when I first studied trigonometry, I only had tables to work with, no calculators existed. Well, any trigonometry book has trigonometry tables. So, I answered my question.
New Planet School I am still thinking about the break section and how everything is worked so that it works within the unit circle..You really explain much better than any other video I have looked at. Im 62 and doing Maths with the OU and you are a very good teacher ...thanks
Great information , love the way you present the graphics, makes it easy to understand. Except the black color background. I think if change it to a lighter color will improve overall. Thank you for sharing your knowledge.
Please don,t make Khan academy as the "gold standard". There are many flaws in their videos. Mostly the instructor keeps blabbering constantly going back and forth confusing the student. Whereas, this video is so clear and exquisitely explained. Fully dedicated to a topic at a time. Thank you.
I hope this is sarcasm. I haven't watched khan academy but this guy here cant stay on topic... so please don't say youre serious when you say this guy is dedicated to one topic at a time.
There are many things that are not clear in this video. I watched this video with a clean slate - I know absolutely nothing about any of this. And soooo many things is this video are not defined that this video is pretty much useless to me.
Clear as mud. ‘Break time!’. Easy, fun. 1+1=2 etc. I followed that bit, but then to introduce the resulting equations onto the unit circle and announce that they represent 30, 45, 60 degrees completely bamboozled me. Why those equations, is there an equation for each individual degree? Find any point with these equations? How, what values and where? Quantum trigonometry.
Could you please tell me the name of the software that you are using to display the content of your videos? I know that in Windows it is Smooth Draw but I can't tell what you are using and what the name of the software is. I am not a Mac user but this software looks excellent.
If you draw the vertical line X=+1 parallel Y axis present for tangent and the horizontal line Y =+1 parallel X axis present for cotangent. The 30°, 45° and 60° of the lines will meet the two new lines. That's the value of the tangent and cotangent. Please correct me if I am wrong. Thanks
Great Video, I like how you used a math break to try to make the concepts more intuitive. you have to be able to grasp the abstract concepts and algorithms(Patterns) or learning any form of math will be a struggle .
Ok maybe it was a cool idea to introduce these concepts during a math break and tell us how easy it was, especially as what he describes helps with the rest of the video but I found it the hardest part of the video to follow see Alex Martino's comment below.
If you please, what software do you use to write the formulas (using a stylus, I am guessing)? I would love to be able to teach classes with the "blackboard" that you use in this presentation.
Hello Christopher. I use two methods to write the equations. If I want to do it "by hand" I write on the "blackboard" using a combination of Omnidazzle and a Wacom tablet. If I want to prepare the equation in advance and have it look very professional, I use LaTeXiT. (I have made a video that shows all of this, and I will upload it today.)
You may have looked at the circle and immediately noticed that X squared Y squared is R squared, but you didn't tell me how we should recognize this? Where did this fact come from?
22:33 I struggled w/ 1/2 x 1/2 being less than 1/2 In school they taught me Multiplication was repeated addition, so I was thinking it should be 1 Being frustrated w/not understanding, I drew a square & labeled each side 1/2. Then as I looked at my square, I thought, how do I get to 1. I drew another box on top & one to the side. That was three boxes & only one more to complete the full 1 square. I finished the square & realized multiplying by a fraction is division. They lied to us when we were young. Now I even know multiplication can be repeated subtraction.
Dude honestly thank you so much... Freaking teachers nowadays just want kids out of their class as fast as possible and don't explain the core concepts.
OK, I am seriously confused on something here. At 36:31 the table shows that sin(30) = sin (pi/6) but also shows that sin(60) = sin (pi/3) but both are showing and equal value of square root 3/2 ... (sorry it is impossible to show the equations so I have to type it out. If I understand this correctly, sin(60)=sin(30)? Am I off track here? New Planet School
Aaron, you are very much on track here. You have found a mistake in the video (thanks to others who have also pointed this out). I have added a comment on that page to clear up the confusion. Thanks!!
Hi. Nice video. At about minute 22:30 you convert the numbers on the left to square root of two over two, squared. I don't understand how you did this. If you multiply by the denominator you get 4 and then you should multiply the numerator by the denominator as well and you get square root of 1 squared (1) multiplied by the denominator you get 2, so 2 over 4. I'm not sure how you got it into the format that you put it in. Even though it equals the same thing.
Your comment is about as spot on as I can imagine, I just spent about an hour trying to work out how he does that even though like you I can see he gets the correct answer. I find this so confusing even your description of it, which seems like a model of clarity to me! I think he just says something like people don’t having square roots on the bottom but that’s easy to fix by just multiplying top and bottom by the square root. Then he seems to do about another ten steps without really explaining why
I realised how perfect math is, I'd like to go back to Pythagoras era and be able to enjoy the beauty of math, today; all that beauty is found in a calculator
Hi. Got a better way to remember to trigonometric ratios: Oscar Has A Heap Of Apple switch the letter upside down to get the other relationship Sine = Oscar/ Has or Sine = O/H Cosine = A / Heap or Cosine = A/H Tangent = Of / Apples or Tangent = O/A Secant = H/O Cosecant = H/A Cotangent = A/O
im looking for someone whi can explain why tangent = opposite over adjacent... like i know why you have to divide the adj and the opp to hypotenuse to get the sine and cosine... but i would like to know why you have to divide the opp and adj to get the tangent
¿Qué pasa con el valor absoluto de la raíz en el minuto 20:56?, si la raíz es par y lo que está dentro del radical esta elevado a exponente par, el resultado sera el valor absoluto de la expresión dentro del radical.
Uhm i dont understand the fraction you did on break time. Could you do more videos about that? and btw at 35:24 how did that became 1/2? is it becoz PI is 3.14.. so its 3.14/6 simplified it to make 1/2? Your website is not working. I wish your website is working so I could ask a question there,.
I understand everything else apart from one thing are we meant to use radians to find out the angle for trig i dont know how to get the angle in the triangle drawn in a circle??
Thanks for the question. I think there are two parts to your question. First, you ask about radians. Radians are just one set of units that you can use when you work with trigonometric functions. But, you could also use degrees, gradians, grade, minutes of arc, or any other units that make sense for you. (Look up "units of angle" on Wikipedia for more.) It is usually most convenient to use radians, but people typically talk about things in terms of degrees, which means you have to get used to converting back and forth. Luckily, that conversion is simple: 1 radian is about 57.296 degrees (360 divided by 2*pi), or one degree is 0.01745 radians. Your next question refers to finding the angle in the triangle. By this I assume you mean that you know everything (lengths of sides) except the angle, rather than knowing the angle and needing to find the lengths of the sides. In that case you need to use the inverse trigonometric functions, which should be built into your calculator. Try it for some cases for which you are sure of the answer. And, putting these two questions together, be sure that your calculator is set in the units you want to use. Very often we can get confused when we think the calculator is returning degrees when in fact it is giving us radians. Let me know if you have any further questions!
Well I think it ’s easier to remember radians as a formula if you have an angle α with can use the formula x rad=π/180deg times the degrees of that angle α let's say α is 180deg and you can simply say that x rad when the angle is 180deg is equal to π which is equal to 3.1415926535793 and so on, but hopefully anyone reading this got the point.Remember x rad=π/180deg times the degrees of that angle α or whatever you want to call it.
Mattie Stark it's a lot simpler once you get up to this level. This is around sophomore to junior level math in high school. I'm sure you've worked with numbers like pi before.
My brain can't concentrate on this. :( I've been trying to pay attention in class but I just can't seem to grasp the point of these, therefore cannot get my brain to digest it.
