Note: I made a mistake in the video. I said that I only use the sine function, but that's not true. its not that i only use sine function, but more like 'I'm only using the sine function out of all other trigonometric functions." I hope this clears up all the confusion.

@fortcraftgaming2136

3 ай бұрын

U forgo cos in da vid

@RailsofForney

3 ай бұрын

@@fortcraftgaming2136 TF are you saying?

@oof2104

3 ай бұрын

@@RailsofForney "you forgot cosine in the video"

I'm a musician and I was 100% expecting to hear these waves

@sournois90

3 ай бұрын

if you're really a musician, name every song

@EdKolis

3 ай бұрын

Variations on the C Major Scale

@JohnAndrewBuyco

3 ай бұрын

@@sournois90 bruh what?

@keenban

2 ай бұрын

​@SeeJay-ji7tqwhat about songs in microtonal tunings?

@HexaflexagonFan

2 ай бұрын

@SeeJay-ji7tq what about music that doesn't use western tuning?

I wish these could be rendered with full detail

@Fire_Axus

4 ай бұрын

i second this

@ianweckhorst3200

4 ай бұрын

Eh, working with Desmos you get used to it

@eyesicecold

4 ай бұрын

Maybe GeoGebra could work?

@user-ro2tm3dp8x

4 ай бұрын

if they actually could the line would be infinitely thin so invisible so a blank paper is a render with full detail kinda

@AdrianBoyko

4 ай бұрын

Try buying a Raspberry Pi because the full version of Mathematica is free for the RPi. I’m guessing that it would do a better job of rendering these.

nothing could've ever prepared me for how smooth y = sin(x) + sin(y) was

@maurolionelmisjuegosyo940

2 ай бұрын

2:13 ye

4:40 This is someone who has seen the true power of sine. 🤯

"At this point you know I'm obsessed with number 9" Words of a Cirno fan, no doubt

@StrikeEagIe

3 ай бұрын

Yuck, i could smell this touhou fan from a mile away Deodorant aisle is that way

@codyburns-so9hx

3 ай бұрын

9 is beautiful, as it is the place value limit in our base 10 system. 9 does a lot of beautifully interesting things

@theocgaming9433

3 ай бұрын

​@@StrikeEagIeor you could just *leave?*

imagine if we could see this in the complex plane

this is so cool and such a vibe with the music and little inbetween captions

@the-mathwizard

4 ай бұрын

I'm glad that people like slower, simpler, and calmer videos. Thank you.

@frosterslime1670

4 ай бұрын

fancy seeing you here looser, apparently we get recommended the same cool videos from smaller channels

@puppergump4117

3 ай бұрын

@@the-mathwizard tbh anything slow is bound to bring people relief from the endless tiktok crap

A lot of these graphs look like that because of the limitations put on how precise they are to the real thing (since points are infinite therefore not every single can be rendered). It can be seen with the small missing pieces that should be there but aren't rendered.

I particularly enjoy y = x • tan(x²+y²), it makes a very nice spiral

@DoxxTheMathGeek

4 ай бұрын

You are right! owo That's amazing.

@Biggyweezer69

3 ай бұрын

I also like this one a lot, it doesn't look like something that would behave so nicely, even desmos has trouble rendering it. Why it creates a spiral becomes clear when we convert it to polar coordinates, we get theta = r^2, or r= +/- sqrt(theta). I also didn't expect it to be so simply expressed in polar.

@parkerblacklock8272

3 ай бұрын

How to get people to crash their computers, Plan A:

@liquidgargoyle8316

3 ай бұрын

i put a nice render of it on imgur a/7yRULrG

@brainsmasher8288

3 ай бұрын

Nice

You somehow brought emotion to showing sine graphs and thats so cool

A lot of these are good easter egg designs

4:06 is just sin(x)=sin(y) and 5:27 is just xsin(x²+y²)=1 (Except the forms shown in the video also have y=0 superimposed as a result of multiplying both sides of the equation by (y-0) )

i love the little comments with each function they’re so cute

@the-mathwizard

3 ай бұрын

Did i just make math cute?

@ahmetemiruludag

3 ай бұрын

​@@the-mathwizardYou come from heavens if you can achive that, you must be Acute angle!

@amberlandball

3 ай бұрын

​@@ahmetemiruludag..

Amazing 🤯I saw someone send the equation for a heart on a valentine card, but this is on another level. Please more.

it goes wibbly wobbly

Math wizard be like: I'll have 2 number 9's a number 9 large

@the-mathwizard

3 ай бұрын

9

@sournois90

3 ай бұрын

6

@plzhelpireallyneedabettern4065

3 ай бұрын

9

@Normal762

3 ай бұрын

6

I do this all the time. I'll choose a function and guess what the graph will do as I add things. I am not alone!!!

4:09 Is actually really interesting: y = y * sin(x)/sin(y) simplifies to sin(y) = sin(x), which can be solved to y = x + 2*pi*k, where k is any integer between -infinity and +infinity, giving a bunch of diagonal (y=x) lines spaced 2pi apart. Since sin(-alpha) = -sin(alpha) = sin(alpha + pi), this can also be solved to -y = x + pi + 2*pi*k or y = -x + pi + 2*pi*k, where k is once again any integer between -infinity and +infinity, giving a bunch of diagonal (y=-x) lines spaced 2pi apart, but translated by a factor of pi.

@INGIE32

2 ай бұрын

🤓🤓

@gito4066

2 ай бұрын

😎😎

You could try "y=sqrt(1-x^2)*sin(10x)", it makes a sine wave that fits inside of a circle

Great vid!!

Awesome video! 👌

Bro this is awesome.

I like these videos cause before the graph shows I take some seconds to think how the function will be, pretty interesting, keep up the good work

It’s pretty cool that for any sine function, let’s say f(x) for example, whenever you multiply x and y it always leaves a line of non values around the origin that “cuts” the graph in two, almost like an asymptote in a hyperbolic function.

Such a nice video. Thanks for sharing cool functions you've found

@the-mathwizard

4 ай бұрын

Of course brother, you're welcome

5:26 - SOMEONE SPLIT THE WATER ON THE HILL!

The 4:05 graph is simple, sin(y)=sin(x)

@the-mathwizard

4 ай бұрын

Beauty lies in simplicity

@shrirammaiya9867

4 ай бұрын

​@@the-mathwizardya I know, just pointing out

@cadekachelmeier7251

4 ай бұрын

With the minor difference that sin(y) != 0 => y != kπ

Intrusive thoughts winning 💀

@Fire_Axus

4 ай бұрын

real

2 ай бұрын

What i dont understand

This was amazing, math wiz! do you have one with cosine? I had so much fun! I went from ABSOLUTELY hating trig to watching videos like these for fun!

00:11 Sine Wave 00:32 Frequency * 9 00:41 Magnitude/Loudness * 9 00:52 & 01:01 Pitch Envelope 01:12 & 01:22 Idk

Now put sum function at the beginning n=x and put any number on top

It's been nine days since this has been posted and I got reccomended it.

super nice man

My personal favorite sin curve is |sin((pi/2)x)|=y^2 because it makes a chain of what looks like perfect circles

Very cool!

wtffff bro thats amzing

With the ones where there’s a y term on the RHS as well as the LHS being equal to y- how does that work? Is the graph not showing a function but just the set of all solutions to that equation? (I did a maths minor at uni but that was a couple years ago)

@aeleron0577

3 ай бұрын

Yes, pretty much. You can simplify these equations to y= something, although the resulting formula definetely will not look as nice. Often enough it will also not fulfill the requirements of a function (each x-value is assigned to at most 1 y-value). Instead of that, the equation might be fulfilled for all y>x or similar.

@projekcja

3 ай бұрын

It uses a numerical method to scan for all pairs (x,y) that solve the equation. Coming up with such a numerical method is really cool and a fascinating problem. I recommend you read, at least the start of a wonderful introduction to Tupper's Algorithm: www.dgp.toronto.edu/~mooncake/thesis.pdf

When I was trying stuff, I liked what sin²(x)=tg(y²) looked like

this is so cool

You can do some equally interesting things with nested trig functions as well

y=sin(9x)+sin(x) looks so satisfying

at 4:06 y=y*sin(x)/sin(y) simplify by y and you get 1 = sin(x)/sin(y) and then mutiply by sin(y) and you just get sin(y) = sin(x)

Y= Sin(9x)+sin(x) is what i call fractal sine or sine sine where the small sine wave from a big sine wave

AMAZING VIDEOOO

I like 2:00 Because this reminds me of how AM radio waves are transmitted. Kinda just a sine wave riding a sine wave.

Some of these are super cool and some of them make me viscerally uncomfortable with how imperfect they are

I want to see this in Desmos 3D now

1:00 IT'S CUBIN TIME!!!

Magic!

Bro I just started my trigonometry unit in geometry, this is cool

4:05 the Ys cancel so ur basicqlly just solving sin x = sin y which will just be periodic straight lines

Would be cool to change the 9 by a variable and then animate that variable to go from 0 to 9. So that you can see how the figures form

@the-mathwizard

3 ай бұрын

That's a topic for a future video.

4:09 it should be simplified to siny = sinx so y = x + n180° or y = 180° -x + n180° therefore it has a crisscross pattern

5:40 I was expecting the roblox epic face because “it’s over 9000” and that reminded me of “zomg so cool, but it’s ovah 9000”

@ninetysixvoid

3 ай бұрын

naah, this is the true "it's over 9000" moment: kzread.info/dash/bejne/hZ2BqraEYZi2mc4.htmlsi=Zo_H0dJSCMw8ZALo

@Chad_Thundercock

3 ай бұрын

Funny enough, that's a meme based on a meme. The original comes from an early English translation of Dragon Ball Z.

You should edit this as an sin(x) Iceberg!

can anyone explain or link to smthn that explains how a graph can have multiple y values?

Desmos is cool but Mathway graphing calculator renders the graphs much more precisely. Maybe give it a try.

Normal graph: 😒 Graph with 9: 🤩

Learning sine waves 😪 Visualising it : 🤩

Cool video! Just a question, where do you get that equation font?

I wish you could do a f(x,y,z) sine function version, so we could see cool three dimensional versions of this.

@ricardoperez8658

3 ай бұрын

sin(xy) is already three dimensional, in fact, a third variable would make the plot 4 -dimensional (though this would be impossible to represent). The reason why you see the xy functions in a plane in this video is that we are just seing a “level curve” (as if you cut the function at a certain height).

Number 9 is the main character

@the-mathwizard

4 ай бұрын

Sure it is, agent 009😎

@biggusdickus1689

4 ай бұрын

This is what the Beatles were talking about

@attackoramic8361

3 ай бұрын

Number 9, Burger King Foot Lettuce.

1:30 ok NOW it gets awesome

Much of this confuses me, but what about the dashed lines? The broken off peaks are weird with sin (x^2 + y^2) (let's square both) is that a visual glitch in desmos?

“Damn son” is my only reaction 😂 I’m in grade school and we use Desmos for our calculations, so whenever I get bored, I just go to Desmos and do something dumb, until it creates beauty like this.

I’m not even going to pretend I understand why those graphs can be made 😂

idk what im gonna do with this but at least now i know that i can confuse anybody without a phd in math with y=sin(xy)

4:08 That one makes sense actually; cancel the "y"s

i think it'd look better if the transitions were immediate, the function could be in a small box somewhere

I was shocked at y = sinx + siny because I thought that finally I found the "circular-sloped" sine wave when I noticed at the same moment that it's not. What I mean by "circular" sine wave is that when every section is a perfect half circle. Does such a wave exist?

2:20 bro thats just tangent

ay try the dancing one - c = b tan(cos(x1)x)

2:01 ITS THE KEYS 🔑 🔑 🔑 🔑 🔑 🔑 🔑 🔑

@the-mathwizard

4 ай бұрын

If you replace the number 9 with a higher number, you'll get even wigglier graphs

y=Sin(x^x)+sin(x) is my favorite (explicit too!)

Can you create gaussian using addition of sin functions? If possible tell function value

You can make infinite infinities with 'sin(X)!=sin(y). This video uses only sin, but cos looks better in my opinion because it's centered.

Let me toss you this one: sinx + sum from n=0 to infinity of n/10^n sin10^nx. Zoom in as much as you like, it will still look like a sine wave

@the-mathwizard

3 ай бұрын

I just tried plotting the graph, but after zooming in a couple times, it's not looking much like a sine wave. Could it be that I've entered the function incorrectly?"

3:40 better infinity is "sin(x) = sin(y)!" (! - factorial)

@the-mathwizard

3 ай бұрын

you're goddamn right, how could I forget to add factorials

y=2^{2sin(2x)}-2cos(y) For a row of... *special items*

@alansmithee419

3 ай бұрын

or replace the second 2 with 4 for some tall chess pieces.

1;5x speed makes a cool beat

Sine function on LSD!

Friendly reminder that math is freaking cool

The third one in the thumbnail looks extremely scary

2:24 dude you can't fool me that's bacon

I’m curious to how the computer is able to calculate y=sin(xy) since the dependent variable is in the equation

@projekcja

3 ай бұрын

Desmond uses some numerical method to scan for all pairs (x,y) that solve the equation. Coming up with such a numerical method is really cool and a fascinating problem. I heartily recommend you read, at least the introduction to Tupper's Algorithm: www.dgp.toronto.edu/~mooncake/thesis.pdf

@Gabriel_JudgeofHell

3 ай бұрын

isolate y or use a parametric

Me when I get to class to do my maths test and I have to graph y=x•sin(x²+y²): 😮 (I'm going to humilliate myself more than ever)

When I tried the y=sin^3(x) in Desmos, I got an error saying “Only sin^2 and sin^-1 are supported. Otherwise, use parens.” How unfortunate, still looks pretty cool on your end.

@omaisajalil7474

Ай бұрын

sin^3(x)=sin(x)^3

no way this has only 1.7k, i thought this would be viral lol. even if you don't like math it's super cool

@the-mathwizard

3 ай бұрын

Thanks, soon those "k"s will turn to "m"s

amazing video ❤, but switching from black background to white one so often hurts my eyes, would be better if it was only black or only white 😅

Those sines are beautiful? Maybe you could use variables so we see how they change in real time?

y=y sin(x) /sin(y) looks like a linear transformation

@quantumgaming9180

4 ай бұрын

Can we prove that those lines are lines indeed?

@adiaphoros6842

4 ай бұрын

y = y sin(x) / sin(y) 1 = sin(x) / sin(y) sin(y) = sin(x) y + 2πn = x + 2πm; n, m are integers. y = x + 2π(m-n) When n = m = 0 y = x So yes, those are lines. The 2π(m-n) term gives the graph its periodicity.

@quantumgaming9180

4 ай бұрын

@@adiaphoros6842 I see. By the way, you ought to be careful when simplifying by y at the beginning since you can lose solutions. There is another line you are missing, the y=0 axis Other than that, nice proof

@Dedicate25

4 ай бұрын

add 1 to that and look at the graph :)

5:07 looks oddly perspective

When I entered one of the last ones in Desmos I got a error saying the fine details haven't been implemented yet.

@nathanoher4865

4 ай бұрын

That’s normal, since it’s hard for the software to plot every little tiny detail, as it’s technically infinitely detailed

Please try inverse functions

(cos(x)*cos(y))^(1/3)>=sin(x)+sin(y)

whoah never seen y^3 =sin (X) before

With the ones where there’s a y term on the RHS as well as the LHS being equal to y- how does that work? Is the graph not showing a function but just the set of all solutions to that equation? Or is there some kind of recursion here? (I did a maths minor at uni but that was a couple years ago) Edit: accidentally posted 2 copies of this comment apparently. But they both have replies now so I’ll leave it

@projekcja

3 ай бұрын

It uses a numerical method to scan for all pairs (x,y) that solve the equation. Coming up with such a numerical method is really cool and a fascinating problem. I heartily recommend you read, at least the introduction to Tupper's Algorithm: www.dgp.toronto.edu/~mooncake/thesis.pdf

@yoelcalev2763

3 ай бұрын

Desmond uses some numerical method to scan for all pairs (x,y) that solve the equation. Coming up with such a numerical method is really cool and a fascinating problem. I heartily recommend you read, at least the introduction to Tupper's Algorithm.

Well try this sin(floor(x)×x)

Biblically accurate sine wave