The true role of the circular functions | WildTrig: Intro to Rational Trigonometry | N J Wildberger

[@dcart77]

Every time I watch one of your videos I feel like I'm going on an adventure. Really appreciate your time and effort making these videos, thinking outside the curriculum box and teach what other teachers won't.

[@njwildberger]

Thanks Tino! It is an adventure to explore the world of ideas. And mathematical ideas are often so interesting, especially when we appreciate that there are new and exciting ways of looking at familiar things.

[@girirajrdx7277]

I am literally crying….such a beauty…wish i had found this video long back….wish i had teachers like you

[@stilingiceland1403]

Already bought 5 books from wildegg.com for my offline study. Really appreciate your courses.

[@federicofresneda7021]

Thank you for posting this videos! Right now i´m following the course of linear algebra. Pure gold.

[@alihammadshah]

Your channel is really great. I am going through the algebraic calculus and linear algebra course and while studying linear transformations (rotations) I came across these functions and this video explains them precisely thank you very much.

[@njwildberger]

Hi Ali, Glad to hear you are enjoying the channel!

[@bastian1833]

Once upon a time, a meter was defined to be the 10 million^th part of a certain northern-half-meridian through paris. That makes a milli-gradian in latitude or in longitude at the equator to be pretty much exactly 1 meter. For that reason, gradians are pretty well suited for surveying tasks and still often used there (and almost only there and nowhere else). By the way, great that you point out that the turn is actually the "natural" angular unit on the circle. I totally agree.

[@chimetimepaprika]

Retro Funk Circle Slam 2020. Bring on the round.

[@JasonQuackenbushonGoogle]

I’m really enjoying reviewing all of this mathematics from a your perspective on rejecting real numbers and avoiding transcendental functions. one thing I’m curious about, as a musician and composer, is how the decomposition of complex waveforms into sine waves and/or the harmonic relationships of pythagorean intervals work out using circs or turns instead of rads or degrees to work out the formula.

[@schrodingerbracat2927]

in this case, angle will be linked with time elapsed. e.g. note 'A' of 440 Hz means every second you have 440 cycles, which is 440 times 360 degrees (or 2 pi radians).

[@JasonQuackenbushonGoogle]

@@schrodingerbracat2927 yes, that’s a really attractive aspect of this way of looking at this because it makes frequency clearer. rather than saying a complex wave form has a fundamental and harmonics which are some multiple of pi-or in a modern electronic composition temporal displacement a la Steve Reich’s phase compositions like “it’s gonna rain” or flanging/phasing in signal processing more generally, as a difference in degrees “out of phase”-tying the sine waves of each of the harmonics, it looks like using turns and turn angles along is more intuitive because it directly corresponds to cycles per second (hertz) which would be the same number as multiple turns of a repeating turn angle equivalent of the sine function. I’m not sure if i am saying that clearly, but it seems obvious to me that this could greatly simplify and make more intuitive the applied mathematics of musical harmony, electronic sound synthesis, and potentially have applications for lossless compression algorithms and the acoustic analysis and engineering of physical spaces and musical instrument resonators.

[@jobersudyobodou9362]

I fiddled with Bhaskara's formula to see if I could reduce the error. As given the peak-to-peak error is 0.00297. With slightly different constants, peak-to-peak error is 0.00211 for 0 to 180 degrees: sin(x) = -0.00068+N@4 x (180-x)/(40500-1.00705x(180-x))

[@vanillaglue]

Awesome!

[@sotkarek]

I agree with you. Traditionally radians are introduced to measure arcs of generic r-circumference (is sufficient multiply the number of radians by r ). In this sense x and y have the same unit of measure after a simple multiplication. But why do we link radians and angles if angles are defined as infinite area in geometry? A little bit confusing. Anywhere in spectral analysis and econometrics these periodical functions are fundamental.

[@braindead3201]

When I learned radians, the reason I was given was the arc length formula which needs radians

[@brendawilliams8062]

Thank you.

[@surrealistidealist]

10:30 So fascinating! Regarding the need for fine observations, do you think this also has potential relevance for probability theory, statistics, computer science and even other topics as well? (I don't see why not! 🤩 )

[@alute5532]

There are other trugnonmetric functions like tan city & other reciprocals G H Hardy ramanunjan's professor Course of mathematics circular functions talks about What is the x occurse in cos x sin x For 2000 years definition was near of an angle thefrom 0 to 360 Babylonian system All classical tables are used As Reticus, x gives different sin cos Independent variable x in degrees Dependent y from -1 to 1 Y = sin x moving uniform on circle but not on proj(y), y coordinates Basakra I approximation Sin x = 4x* (180 -x)/40500 -x*(180-x What drove lit of development leading to Rerticus tables with 10 places Astronomical uses Trigonometric is brushing linear motion& circular motion connecting these two Connects uniform circular motion with linear motion X side no motion ambiguity linear But on other side- Circular there's slot of possible Infinite ambiguity Because there's different lot of unit systems use to measure where we are on circle Degrees radians New Gradians , turns? Number of different possiblies measure along the circle even if Interested Some better for pedagogical work Other better for advanced applications --- Ways go uniformly round circle Babylonian system 360 decimal base 60 Divide things more efficiently By 2, 5,..40,60 From calculus There's an advantage of framing the sin function in terms of radians We need to understand uniform circular motion Doesn't have to be framed in terms of gradients Only relevant after 2nd year doing Fourier analysis No need to deal with transcendental issues (like pi) Issue 4th era lot of places where pick is involved where they don't need to be involved Unnecessarily complicate Connect with transcendental aspect that you really don't have control over These infinesimals numbers go off to infinity renders outside the realms of pure mathematics Why radian systems What are the alternatives Highschool mathematics Addressing the question what should they learn in context of uniform motion (physics)

[@escher4401]

Where is the rational fourier analysis?

[@balaportejean7015]

thx sir Jesus loves you Believe in him and repent !