How to rotate any graph by any angle

[@uncleben7306]

This video is really cool, you have a super simple derivation for the transformation too. One thing I think you should have included was why using a rule to rotate the point counterclockwise ended up rotating the graph clockwise. It was because plugging the new expressions in for x and y was basically saying "the counterclockwise rotations of these points satisfy the equation." So the said points would be a rotation in the clockwise direction from the original equation (very similar to how replacing x with x+2 in a function actually moves the graph to left by 2, instead of the right). To go in the standard counterclockwise direction, you can plug in negative theta and simplify with sin and cos rules. Also, it explains why the parametric equations still rotated counterclockwise, because you replaced the functions with the expressions rather than x and y, so the values that were equal to the new x and y rotated counterclockwise, instead of the counterclockwise rotations of x and y satisfying an equation. Again, great video. You definitely deserve more subs for this quality of video and explanation.

[@fahrenheit2101]

I knew some subtlety had to have been glossed over - thanks for this. Still a little weird to wrap my head around though.

[@uchinanchuu58]

You answered the main question I had about this video. Thanks!

[@may21136]

Yep. Given that positive theta = anticlockwise, we should ideally start with the transformed coordinate point (x',y'), rotate the point (x',y') back to our original coordinate system (x,y) in a clockwise direction (wherein negative theta comes), and then use the equation y = f(x). The final equation should be consisting of x' and y' terms. What this guy did, is that, instead of finding the locus P' (x',y'), he ended up finding the locus of P' conjugate (x',-y'), entirely going against the initial purpose.

[@zackattack9228]

Thanks uncle Ben🙏

[@rolosilver3256]

UNCLE BEN?!

[@OrangeC7]

"All I ask for is infinite precision, is that so much?" Every mathematician ever

[@omargoodman2999]

Heisenberg Uncertainty Principle: Yeah, about that...

[@someoneonyoutube8622]

@@omargoodman2999 Gödel’s incompleteness theorems & Turing’s halting problem… we need to talk

[@FireyDeath4]

See if you can run Desmos on your personal hardware, get a chunkier graphics card and make the limiting parameters bigger

[@NoerLuin]

Fun Fact: in this case it is not about precision, the reason why it looks wrong is aliasing (the signal processing kind). The simple version is, that in each pixel on the screen there are multiple red lines, which cannot be shown correctly to you.

[@someoneonyoutube8622]

@@NoerLuin what if someone invented a computer that could rotate pixels acording to the direction needed to display the best resolution for a given image

[@pkmnhx43_27]

Finally, I can rotate the line y = x I've always wanted to model the values of y where it is twice and much as x, but never knew how to rotate it, I can finally live in peace

[@incredulity]

Lol

[@user-pr6ed3ri2k]

tan(a)x be like

[@capsey_]

@@user-pr6ed3ri2k nah dude, i use noodle technique, it's taking a raw noodle on a paper, spinning it around and drawing what it looks like on canvas with oil paints

[@dukeofhollow5541]

Also y = 2x and y = 0.5x graphs be like

[@reeb3687]

@@incredulity is your username dakota? it uses letters ive seen in dakota

[@IlTechnoDashlI]

For those people who don't want to watch the whole 16 minutes: 1) Replace all the X's in your function with "x cos(Θ) - y sin(Θ)" 2) Replace all the Y's in your function with "x sin(Θ) + y cos(Θ)" 3) Set the "Θ" parameter to whatever angle you want your graph to be rotated by And that's it!

[@cemmy410]

Thank you! The video topic is very interesting and I would have watched the whole thing but I had to tap out about 4 minutes in because the pitched-up voice is a sensory nightmare 😩

[@Dark-jn2pg]

Thanks so much

[@kelly4187]

And if anyone has ever encountered a rotation matrix... You already know how to do it lol. It seems a weird choice to go through this and not at least mention it at the end, instead choosing to go through a million examples when one or two would have sufficed.

[@starfeast]

That's literally a matrix. Thank you for saving me 14 minutes.

[@manioqqqq]

Add the parametrics

[@stealthgamer4620]

I really like that he basically taught the polar coordinate plane and system without actually using or saying that it is. Props to this person.

[@fuschia-draws]

all while answering an age-old question math enthusiasts always ask!

[@withjoe1880]

Desmos can use degrees if you open the menu (wrench in upper right corner) and change from radians to degrees. You can also changes axis limits, ticks, polar, and more.

[@Sahl0]

needs likes cos important

[@AwesomeEv]

radians usually works better because you don't have to change the axis scale for a sin function specifically

[@user-iz5pd7tj6q]

​@@Sahl0 I think its sin important

[@Sahl0]

@@user-iz5pd7tj6q inverse tan important

[@jwjustjwgd]

You can also just put a degree symbol after a number while in radian mode and it will calculate that number specifically as degrees

[@jacobbaer785]

One thing to keep in mind is that whenever you rotate a graph, it likely is no longer a function (if it was one to begin with). Some exceptions I can think of are straight lines, and sin and cos (rotated no more than 45 degrees). Otherwise,the curve will "bend over itself" and the same 'x' value can result in 2 different 'y' values. In other words, functions when rotated will, with some exceptions, always become implicit equations.

[@notamouse5630]

And the proper solution to that is no longer thinking of it as a function in the cartesian plane, but instead the polar one. y=f(x) -> r=f(theta) then rotate and it can be a function. Or a parametric equation.

[@astralnekomimi]

This is one way to define that a function is one-to-one: a function is one-to-one if and only if it can never be rotated about the origin in such a way that it is no longer a function.

[@AliAhmed-ez2zy]

@@notamouse5630 Agreed, that's how I approached the original problem; parameterize your equation to make a vector in ℝ² as a function of t, and then apply the general rotation matrix in ℝ²: Rot_θ = {{cosθ, -sinθ}, {sinθ, cosθ}} So for a generic vector valued function v(t) in ℝ², the rotation would just be (Rot_θ) v(t). It's a generic linear algebra approach to the problem that yields the same results.

[@kelly4187]

@Astralnekomimi not quite. Y=X can be rotated up to 45 degrees and still be a bijection.

[@rashid.harvey]

This was missing, you can't really rotate all functions like stated at the beginning of the video

[@WhyneedanAlias]

I actually found out how to do this quite recently. I was playing around and noticed if I change the x in y=x² to x+y and y to x-y I would get a rotated parabola. Then by changing the ratios to like 5x+3y I'd get different rotations but they'd also always get scaled by some factor. So I also added complicated scaling factors until I tried using trig functions to scale the axes and it became so much easier. And after having taken a linear algera class it also makes much more sense because it is basically just applying a rotation matrix to [x,y]

[@kelly4187]

Still, nice work! Maths is supposed to be something we play with, not simply memorise to pass tests. No matter how hard it gets, you're doing it right!

[@shmuelalexis9836]

This questions, of rotating the graph, have been in my interest for long time. I always though a general procedure exist - glad I found your channel. Great work.

[@int16_t]

So, basically you apply a 2D rotation matrix on the curve of the function. I find it interesting the inverse of x^2 (which is an even function) is sqrt(x) which is rotated 90 degree clockwise, and the inverse of x^3 (which is an odd function) is cuberoot(x), which is rotated 90 degrees (either sides), and flipped horizontally. While the inverse of 1/x is 1/x itself. Cool!!

[@judecarter6095]

In fact every inverse function is equivalent to a pi/2 rotation and a reflection in the x axis, because that's functionally the same as reflecting in y=x.

[@angeldude101]

Alternatively, you multiply by a complex number. Using a matrix let's you represent arbitrary linear transformations, but complex numbers restrict you to just rotations (and scaling if you let them be unnormalized) which is perfectly fine and more efficient if that's all you need.

[@aliensoup2420]

Yeah, he's kind of lying when he says he doesn't use matrices. He is writing out the matrix operations long-hand as a new function, but he is still applying the standard rotational matrix transformation. It seems that a sophisticated graphing application could perform the proper substitutions without the need to write it out yourself. In a sense, he is defeating the purpose of layered abstraction, which is the general basis of higher mathematics.

[@jaythegreat9211]

@@aliensoup2420 You do have to remember the target audience of this video is people in lower levels of math

[@kelly4187]

Then perhaps he should have not said anything about matrices in the description, and actually mentioned them in the video at the end. Tease them with the method and examples in the video, but then say "you know how I said we rotate the x-y plane not the curve... Well there's a more general way to transform the x-y plane..." And at least simply name drop

[@DoctressCalibrator]

I couldn't help myself but laugh when you added this modified voice that said "Shut up and tell us already." You did a great job!

[@trippstreehouse]

Thanks for the demonstration, wish you didn’t pitch shift vocals.

[@sander_bouwhuis]

You blew my mind with this video. The visual presentation makes it extremely clear that it indeed seems to work for all sorts of equations.

[@igxniisan6996]

YOU DON'T KNOW HOW MUCH I WANTED THIS PARTICULAR VIDEO FOR DECADES BUT NO ONE MADE IT I WAS SO DISAPPOINTED... FINALLY I CAN NOW DIE IN PEACE ☮️❤️ This is what we learnt in Electromagnetic Field Theory course in details, it's called "Tensor", Tensors let you do this! This guy just derived it in a simple way, if u add one more axis it will become the tensor rotation formula.

[@kelly4187]

... This is also just a simple rotation matrix from pre-college linear algebra.

[@redbeaniemaths]

Part 2: kzbin.info/www/bejne/lXW8ip2ZnpeEptk&ab_channel=RedBeanieMaths

[@Sirmrmeowmeow]

part 3 soon? D:

[@Sahl0]

thats a banger of a video, what

[@idkyet9458]

how do i make the parametric draw itself?

[@Thomfamily5]

whats MOB? what does the function stand for? how does it work?

[@magnusalferes1143]

I need to thank you so much for this, I've been working on a video game for a while now and decided that I would spawn things as I go rather than hand build in the editor. You have bestowed the power of rotating graphs upon me and now I can build using arrays and rotate after, simply amazing!!!!

[@muffinconsumer4431]

No pitch shift = 7x better video

[@sportsloverbaseball]

What does it matter? Maybe they just don’t feel comfortable with their voice being heard

[@muffinconsumer4431]

@@sportsloverbaseball And I don’t feel comfortable not hearing it

[@EHMM]

@@muffinconsumer4431 Literally only you.

[@muffinconsumer4431]

@@EHMM despite tens of other comments to the contrary. Riiiiiiight.

[@EHMM]

@@muffinconsumer4431 Literally only abnormal people

[@pseudonym8762]

never have i ever thought i would want to know how to rotate graphs like this. 10/10 gonna send it to my friends now

[@may21136]

I know that derivation of sin theta cos theta for rotation is very confusing, and I avoid doing it that way because of this. I advocate for the usage of *complex numbers* for this purpose. Complex numbers make the concept of rotational transform much easier to grasp, but you need to learn complex numbers before doing a rotational transform with it. Math is fun. If you learn something as intricate as complex numbers, you will find other harder things getting easier for you (such as finding rotated coordinates in this case). Rotation is just a special case of complex number multiplication.

[@Wishbone1977]

Honestly, when he began the explanation of how to rotate a single point, I was expecting the explanation to wind up in complex number territory and was mildly surprised when it didn't.

[@kelly4187]

I think it's because of the level of the target audience. But to say "without using matrices!" In the description, and not at least even namedrop a rotation matrix, which is EXACTLY what he did here? Travesty.

[@RichConnerGMN]

cool video. why the pitch shift

[@mrmaaf1443]

Really cool content but that voice changer is really annoying, like borderline unbearable

[@stinknamazing]

I really enjoyed this! Great job! Such fun to watch.

[@jaafars.mahdawi6911]

Just how much energy can be felt in a simple, yet neat video like this one? Keep it up, man!

[@Sebbethy]

I love this video, I really do! So it hurts me to say there's probably a mistake as from 8:50: In the lower left corner shouldn't it say "y ---> X sin(θ) + ycos(θ)"?

[@quantumgaming9180]

You are right

[@ibrahimElKhalil55]

If we use a slide to move the "diagonal sine" diagonally, wouldn't that make it look like a moving escalator?

[@jungtaemin1639]

You would have changed my life 10 years ago And you just made maths 10 times cooler for me, a mechanical engineering student

[@kelly4187]

Learn linear algebra and you can do all of this and more in a simple formulation.

[@jungtaemin1639]

@@kelly4187 i already did, but this video tells me i could have figured it out during middle school using more basic maths. I really wanted an answer to this problem and never got to actually solve it nicely back then

[@andrewsemenenko8826]

I figured this thing a long time ago, partially by myself when I was in school (currently in University, making games) Was really curious how it works back then. Thank you for the explanation to others who are as curious as I was! Good luck with the channel

[@supramayro434]

Українця тутка навіть не думав знайти

[@dewanthenmalai4232]

You can also derive the formula using the complex domain. Define a complex function of a Real variable as Z(x) = x + i*f(x), then since rotation in the complex plane is just multiplication you multiply Z(x) by e^(it), where t is your angle. When you do that, the Real and Imaginary parts of your new rotated function are identical to your transformation rules.

[@lycheejuicelichigaming2263]

First thing in my mind

[@rusgon]

What a profound and clear explanation! Thank you!

[@guillermogil3391]

This is amazing, beautiful and such a perfect explanation!!

[@Aditya_196]

🙌 you have my praise from all the math holic kids and myself for creating this video

[@1234567zeek]

I've been fighting with this for about 30 years ... thank you!

[@spicca4601]

20 years ago I was a high school student. And I ask exactly same question to my math teacher, but he even didn't understand the question. And after 20 years now finally I get an answer to this. Thanks a lot!

[@eishwarpawar4171]

This is a nice intuiative demo, great work

[@Catkid]

What is the MOB function I googled it and didn't get anything

[@Ilmari_Hirvonen]

Based on the voice I thought that this video was from 12 years ago

[@mxsteri0]

you were 132 months off :]

[@Dhruvbala]

I think what you derived is the inverse of what we want, transforming P’ to P.. since we get points that follow x’=(y’)^2 _after_ (rather than before) rotation. We should instead have solved for x,y in terms of x’,y’, substituting these expressions in the original equation y=x^2 Makes sense as the graphs are later shown rotating in the negative direction. If we want to rotate by +theta, we could just negate all the thetas in the expression Nice video, in any case

[@tuxat_]

this has the same vibe as being lost at walmart and not being able to find your parents.

[@jakubw.2779]

Oh my god, this is amazing, i'm almost a decade after my education, but this made me want to study maths again and i'm not even joking.

[@kelly4187]

Did you not learn linear algebra? This is just a rotation matrix. I did that in high school.

[@elimartin9268]

I found an easy way to put it into Desmos, have different equations: defining the original function before rotation (“f(x)=…”), defining a variable (“b=…”) and the function after rotation. And preferably, put it on “degree” mode. For the parabola at a 45º angle, it would be: f(x)=x^2 b=45 x*sin(b)+y*cos(b) = f(x*cos(b) - y*sin(b)) Change variable “b” to however many degrees rotated you want and change the “f(x)=…” equation to whatever you need to change it to and the rotated equation will update with it. Setting it up like this will also make it so u only have to update less things whenever you want to make a change

[@allegrobas]

Wow!! Thanks for a great video. Love your voice !!!

[@atrus3823]

Desmos has another feature which is very handy for working with parametric functions. You can define P(t) = (f(t), g(t)) and then do P(t) in another cell and Desmos will draw points meeting that definition over the supplied range of t.

[@syre7608]

i couldnt listen to this voice for 1 minute

[@V11MonstersMSM]

Probably he got any grapes

[@udomabasiekeme]

I do can, it's beautiful ❤

[@JonnyBoi957]

Cap ​@@udomabasiekeme

[@brayanxd4547]

​@@V11MonstersMSM"waddle waddle"

[@BITniki]

I love how well you explain how the rotation matrix works!

[@localidiot4078]

I loved discovering this in desmos when i was in high school. It was such a ureka moment for me. Now my favorite method is turning everything into a vector, then you don't even need the trig. it really helps simplify the equations, and it helps me intuit dot = cos and cross = sin

[@theblinkingbrownie4654]

Can you elaborate on the vector method? I also did this in hs but have never thought of that

[@letronix6243]

This video was what I was searching for weeks ago before I came up with my own way.

[@hrishikeshaggrawal]

it's like i ask myself a question and somehow a couple weeks later someone delivers. this has happened four times in a row now

[@mraoz8706]

finally, I can spin x^2 + y^2 = 1 after I'm struggling for years

[@tttoastbut]

wait so is this just a two-dimensional rotation matrix? Like, for upper dimensions you just need to add 0s or 1s, depending on which plane it is rotating to. Is it?

[@trevorallen3212]

Tip: If your using desmos if you wanted it based on degree angles set x degree = x*pi/180 when in radian mode on the trig functions.

[@jonas_the_lost]

Thanks, I didn't know this was possible. I've tried before and failed miserably so thank you for giving me the answer that I thought did not exist.

[@emmettdja]

Very simple. Just add cos of the angle to x and sin of the angle to y...

[@TheXientist]

"without matrices!" what you described is exactly the 2d rotation matrix but just formatted differently

[@polyhistorphilomath]

You can also just use some functional equations and inequalities. Suppose we want to define cosine in terms of sine, or vice versa. Set c^2 = 1-s^2 Now if we have a good value of s, we don't need c to appear anywhere in our rotations. what are some valid values? well s should vary between -1 and 1. We can see that the coordinate transform is just giving us a linear combination of x and y. The scalar coefficients might as well be c and s. Let u = (1-s^2)x - (s^2)y . v= (s^2)x+(1-s^2)y. As it is, this will only cover one quadrant. But if you flip the sign of the first term in both u and v, you get the corresponding quadrant across the y-axis. Flipping the sign on the second term in each will put us below the x-axis. By the two combinations of two possible sign changes we get 4 possible quadrants. Great. Now just keep s between 1 and -1. Substitute u for x and v for y. if it's easier, just rewrite your original expression as a level curve. let y=f(x)=x^2. Now let g(x,y)=x^2-y. you can graph this by entering 0=g(x,y) in most software. If so then 0=g(u,v) will rotate the figure smoothly as s varies. again, just flip the signs to cover the other quadrants. [edit] I should add that the constraint on s isn't arbitrary. if |s| > 1 then the rotation is no longer rigid...that is, the shape is not preserved without deformation. As you can probably guess from the graph of y=sin(x), this is going to cover all possible rotations before you run out of s values. If you only let s vary from 0 to 1 then stitching together all the various sign permutations should cover the entire range of angles. [clarification] To get a mathematically positive rotation, let s vary from 1 to 0, 0 to 1, 1 to 0, then finally 0 to 1, bringing you back to y=f(x). Just switch to the next quadrant when s reaches either 0 or 1.

[@Killerkraft975]

This reminded me, that in computer graphics, coordinates are represented using matrices and you can compute rotations very easily. If rotation is in angles however, this method is required.

[@WaltherStuzka]

A simple example - rotation by +/-45°: y' = 2x' with x' = 1/√2 · (x - y) and y' = 1/√2 · (x + y) gives y = x/3. For example, the point (3, 1) lies on the line y = x/3. After a +45° counterclockwise rotation, this point will lie on the line y' = 2x'. Similarly, the line y = x/3 is just the same as the line y' = 2x' rotated by -45°.

[@KekusMagnus]

baby's first rotation matrix

[@hub3530]

As an Algebra 2 student I am flabbergasted by the ludicrous graphs that were previewed.

[@howlu9086]

To do this I write the function in parametric form then I multiply it by a complex number for example rotating y = x^2 by 45 degrees (t, t^2), (t + it^2) * (cos 45 + i sin 45)

[@omargoodman2999]

Desmos can't do _i_ in the graphing calculator. So it needs a... less complicated approach.

[@howlu9086]

@@omargoodman2999 yes you are right so you can just do it manually because there are always only 4 multiplications in total.

[@fireflightphoenix8710]

What's the MOB that you mention near the start of the video? 2:37

[@jennicawilton4322]

@RedBeanieMaths Really fun video. Thank you. However, you have a typo in the bottom left at 8:52 so when I tried to apply it, it didn't work. You've got y --> ysin(theta) + ycos(theta). Took me a while to realise what was wrong. Hope that helps.

[@rehandrone7146]

So cool Love the video

[@InAMinMaths]

Rotating the plane 90 degrees clockwise almost replaces the x axis with the y axis and the x axis with the y axis, but the x values on the new y axis would be running positively down. So it needs to be inverted. Hence, inverse functions and why you change out x and y algebraically. Thanks for the fun video. 2:58

[@Dhruvbala]

Ah, so I’m not the only one who saw that. And later in the video the graphs are shown rotating in the negative direction. Thanks for the sanity check

[@dschamp5]

Crazy crazy crazy how I was JUST looking at my old writeup of this proof seconds before finding this video. Didn't say anything or look up anything even remotely related to this. Just looked at a physical paper in my notebook with this proof on it, then this video is reccomended to me. That's absolutely nuts.

[@pauselab5569]

my calculus book gave a nice answer to this, you can write the function in polar coordinates which makes it easier to rotate then switch back.

[@supersaiyan2]

I've always wondered how you could rotate a graph, this video answered that question!

[@mrsqueaksrules]

In the words of the great Vincent Vinesauce, "SPEEN"

[@williamfeng9808]

The method I have always learned is convert the graph to vectors and apply a linear transformation, which basically does the same thing.

[@asparkdeity8717]

And for complex values functions residing in the complex plane, a rotation so much easier as it is simply given by multiplying the function as: e^ik f(z) to rotate f by k radians ANTI-CW about the origin, given a suitable branch of k

[@scoutgaming737]

It's beautiful I've looked at it for 5 hours now

[@LheannMichelleFlorento-xc7ux]

The "ShuT uP AnD TeLl thE wOrD it IS" was funny 😂

[@mcpecommander5327]

You can change desmos to use degrees btw Also, for graphs it’s much more efficient (and in my opinion simpler) to represent the graph as a parametric, not to mention it’s actually doable to graph it by hand

[@ValkyRiver]

You’re voice sounds so cool!

[@Dillbeet]

The voice changer kind of cheesy

[@ahmedaref3577]

I tried this for functions like: y=x and y=x^-1 and it didnt work and for functions such as sin(×) and cos(x) it seems to somehow distort the function maybe i did something wrong? But other than that it works just fine

[@omargoodman2999]

Did you happen to change the X and Y axis scaling? I'm playing with the formula, but I'm finding that with graph settings where X and Y axes are scaled differently from one another, the rotation distorts because one dimension of the graph is "stretched" relative to the other. I'm trying to work on a general transformation that can take in the X_axis and Y_axis ratio, as well as the pixel Height/Width ratio to account for different screen size and how wide the formula bar on the left is set to, and adjust all parameters accordingly.

[@autaj]

This is too good, your videos are not boring at all

[@petelok9969]

Great tutorial. Can I ask, to graph in something like excel, is it just a question of separating the x and y terms? I can see the staircase being tricky. I'm interested in rotating an ellipse 😀

[@kelly4187]

Let theta be your dependent variable and plot x,y on a scatter plot

[@PlayNowWorkLater]

Interesting video. What I really liked was in the beginning, with then chalkboard background how you had the x and y coordinates in the lower part of then board changing as the parabolas etc on the actual graph changed. But when you moved on to the Trigonometric functions they just stayed the same on the bottom as the drawing rotated would be great if that could be made visual too

[@saltterrae8188]

This great production uses the derived clockwise point rotation equations for the new coordinates as functions of the original coordinates. One must substitute things that are equal to each other. To replace the x and y in the parabola you need expressions for the old coordinates as functions of the new coordinates. They can be obtained by "rearranging" the equations we do have. If done, they turn out to be just the same except that the signs on the two Sin terms are flipped.

[@Moogie237]

Oh my god. Years ago I pondered with a classmate of mine in algebra 2 whether there was a way to rotate a graph like a parabola and they were like “probably not.” I finally have the method.

[@sincostan999]

lol this reminds me of when i was in year 7 randomly asking my maths teacher if there was a formula for graphing an ellipse. i actually DID learn it a few years later which was pretty cool!

[@utuberaj60]

Superb. I think I will learn to use Desmos to play with graphs like you did. Thanks a lot👌👌

[@kelly4187]

I recommend geogebra instead. It has many more functions allowing you to plot dynamical systems with slopeField, and do dynamic geometry such as constraining points on lines etc.

[@reubenmanzo2054]

The rotating cubic looks hypnotic.

[@Georgln]

I’ll try spinning, that’s a good trick

[@BrennaButcher]

I used a circle that ran through both points p and p’. Then found the arc length from x to x’ using the formula “L=pi*theta*r/180” Then set that length L to the integral for the function of the circle, from the bounds of x’ to x. Then solved for x’. Plugged x’ into the function for the circle, to find y’. My final results were: x’=sqrt(x^2+y^2)sin(arctan(x/y)-pi*theta/180) y’= sqrt(x^2+y^2)cos(arctan(x/y)-pi*theta/180)

[@saltterrae8188]

Interesting. The Desmond shows that this acieves a clockwise rotation. Yet the individual points presents a counterclockwise rotation!

[@MrNess2911]

Great job Dexter! You've a new subscriber!

[@kratos861]

Another way to do it in your head is to figure out the equation of the new axis line, so for example if you want to move it 45 degrees you just substitute the new x axis which is not x=0 its x-y=0 and y axis is x+y=0 substitute x and y in any equation to the origin with the equation of the line around which you need to rotate and bingo, it helps if you can remember the cos and sin values in 15 degrees interval for example the x axis at 15 degrees become x= ((root 3 -1)/(root 3+1) )y and y is the inverse of it, substitute in the original equation and you get the graph rotated to around that axis.

[@arjunjain87]

Can someone please just help in how to do this in Desmos, i typed in the same code but its showing me “Too many variables”, im not even able to add the range 0 to 2pi to Theta… 😢😢

[@momeet6965]

I had this same thought experiment back in high school, I think I googled if it was possible or not and then forgot about it. Now I'm kicking myself for not trying to figure it out because it's so simple. Thank you for this video, my high school self is ecstatic right now (and current self too).

[@Nagibator6000LoL]

Nice, now I can rotate x²+y²=R² graphic

[@ItsaMe444]

You can also multiply a rotation matrice with the vectors of the graph (x,f(x))

[@GuruCodeWriter]

Funnily enough many precalculus courses teach this and will put this on a final. And if not teach the topic it may be somewhere in the back of a text on precalc or in the analytic section with conics. It can go even more in depth such that you need to find a graph that isn’t rotated FROM a rotated graph. The process involves not rotating the graph back but rather rotating axis. Same idea and everything but a more technical term. That’s actually how you derive the equations used in the video. There are even ways to do this without knowing the angle using a fancy equation involving the double angle of cot. An example question I had on mine a while back was something like giving you the equation x^2-y^2=1 and find the right graph rotated 45 deg. I remember that because the test makers didn’t have a right answer choice for it.

[@PunmasterSTP]

As @uncleben7306 noted, it was a bit confusing how the original derivation showed the original point being rotated counterclockwise while the subsequent graphs were rotated clockwise. But in any case, I think this was an outstanding video, and thank you so much for making and sharing it!

[@whisperingocean.]

Hello there. Would you mind to explain why that is the case? Why it rotates clockwise instead of anticlockwise? I have reread uncleben's comment 7 times, but I struggle understanding their last paragraph? Thanks

[@PunmasterSTP]

@@whisperingocean. Yeah it's pretty confusing, and I'm not sure if I could explain it any more clearly. Though this might not be a perfect analogy, I'd think of someone parachuting while the wind is blowing to the west. In order to end up at their target location, they'd need to jump to the *east*, so that the wind would eventually take them to the right spot. I'm sure there's much better explanations than that, and perhaps it'd be worthwhile to google or search KZbin. In any case, I hope what I said could help at least a little.

[@neologicalgamer3437]

I'm so sure that sin thing simplifies to something really beautiful, I just don't wanna do it

[@Jacob-vl6ts]

Yes! I finally have a vague concept for how this works

[@naitikshukla2020]

But what about the angle convention i.e. anticlockwise-> +ve or -ve?????😢

[@단무짘선생]

hey can you explain a graph that’s distance is A from y=x^2?

[@diegogiusto1326]

I didn’t know quasimoto made math videos on yt

[@jixpuzzle]

Absolutely Legendary video man! Now I'll go crazy! Fucking love mathematics. Incredible video! Incredible channel!