Is there a way to make this so I am rotating a point. Like say I have a point (2,1) and I want to rotate it 90 clockwise around the origin. I want to create a visual for students
I actually need this solution for an application I'm working on. The trouble I'm having is how to map the base function (linear, sine, whatever) to the modifying rotation function. Though this video is good for showing how to model that in Desmos, it's really unclear how those two separate functions are being combined. Perhaps a step-by-step would have shown this better?
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
This may be a bit late, but I was wondering what the algebra was behind finding the g(x,y) function as it looks like it uses the idea that to rotate a function around the origin you replace x with xcos(A)-ysin(A), but I am unsure about how the x-sin(a) and dividing the whole equation by cos(A) changes how to function works.
I made that video quite a while ago now and I have lost the algebra that I did to build what was going on. I recall that the equation in desmos that you see is a simplification of many lines of code and that is what it came out to so that it could be done in one line instead of many. However, this file was an earlier version that might be more instructive for how it works to rotate a function by manipulating the variables. www.desmos.com/calculator/gtdg39ojud
Hello, I'd really like some help in this matter. So I have gotten the rotated function, but it is in terms of G(x,y). how do i integrate this function (the function is only a 2d function yet it has 2 variables)
Hi, just a quick question, can you have this series of equations appear on the same document more then once or should it need some changed variables to adjust? I can't see to make two lines with the series of equations used in the first link of the description.
Try using this method instead. I used capital X and Y to do the rotation, but you could easily add lines defining any other corresponding variables to rotate a second equation. www.desmos.com/calculator/gtdg39ojud
Sorry it took me a while to get back to you. In order to rotate a graph like yours you should replace the x with xcosA - ysinA and replace the y with xsinA + ycosA where A is the angle that you want to rotate counterclockwise with the rotation centered at the origin. Here is a link to a graph doing this. Hope this helped. www.desmos.com/calculator/sjrdqyvgf4
I really need to make a video of the changes to do that. It is the most common question that I get. Here is a desmos graph link of how... video will hopefully come soon. www.desmos.com/calculator/ldhfhkqgkw
Nifty ! How might you go about rotating around ANY point that is perhaps already following a curve ? I'd think you could just add to the x & y such as "y = g(x + p1.x, y + p1.y)" but something is not right.
I get this question often. Check out this small change to the file that should allow you to rotate around any point. Video coming soon. www.desmos.com/calculator/ldhfhkqgkw
I just describe the equation in parametric form, and multiply it by a unit complex number w, with my desired angle. Works like a charm. Doesn't work for implicits (not to my knowledge), though. I wrote my own complex number lib in Desmos kinda for this purpose.
Hi this equation worked really well for me, but I was wondering how you found out that xcosa-ysina and xsina-ycosa was what you had to replace x and y with to make a function rotate? Is there a derivation or was it mostly just guess and checking?
I can't derive it all in a comment but here is a link to a paper that does a fantastic job of it. math.sci.ccny.cuny.edu/document/Rotation+of+Axes#:~:text=Coordinate%20Rotation%20Formulas&text=x%20%3D%20%CB%86xcos%20%CE%B8%20%E2%88%92%20%CB%86y%20sin%CE%B8,x%20sin%CE%B8%20%2B%20y%20cos%20%CE%B8.
Hello. This is super helpful in general, but I am in the middle of a project where I need to do this to one side of an inequality. I’m making a flame-shape and it moves along a sine function. I’m trying to make the flame “blow in the wind” essentially.
What is going on with the syntax for the s(x,y)=g(x,y{y=0}) line? I'm not sure I understand what it's supposed to do. When I change it, odd things show up. When I remove it, it doesn't seem to make a difference.
Good job noticing that line. I had left that in from when I was tinkering around trying to get it to work. It is not needed in the final version. What it was meant to do originally was to graph the function separately when y=0 whenever it would normally be undefined by replacing it with the g function. This wasn't needed in the end though and I just forgot to remove that line.
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
Just replace the x with (xcosA-ysinA) and replace the original y with (ycosA+xsinA) then make a slider for A. Using the A slider will rotate your original inequality.
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
Hi sir! thank u for this video, but are we able to know the function after rotating the angle? I'm trying to find a function with the points that I have plotted
Not really, the closest you could get is looking at line 11 in the desmos file linked in the description. Most of the time, your rotation will no longer be a function of one-variable [it won't pass the vertical line test, so you can't always have it in the form y=f(x)]. But, look at line 11 and see if you can build an equation for what you need. Otherwise, check out my video on regressions and that may actually be more of what you need in your example.
I was thinking this over again and I think that I thought of a way to do it. Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
How do you enter an equation that is implicitly defined in your program? The way you have set it up makes the user enter an explicitly defined function.
The way I have it set up in desmos will only allow explicitly defined equations to be evaluated this way. I guess a more accurate title would be "How to Rotate an Explicitly Defined Function | Using Desmos." I can't think of initially how that would be done.
Take your original equation and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
I added that feature to the graph after seeing your comment. Look in the description of the video. There is the original Desmos link and the new link named " *Rotate Any Equation Around Any Point.* "
The sin graph rotated makes an unfortunate shape lol
Is there a way to make this so I am rotating a point. Like say I have a point (2,1) and I want to rotate it 90 clockwise around the origin. I want to create a visual for students
Yes, I don't have time to make a video right now, but here is what I have worked out. www.desmos.com/calculator/ka2serahn2
I actually need this solution for an application I'm working on. The trouble I'm having is how to map the base function (linear, sine, whatever) to the modifying rotation function. Though this video is good for showing how to model that in Desmos, it's really unclear how those two separate functions are being combined. Perhaps a step-by-step would have shown this better?
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
This may be a bit late, but I was wondering what the algebra was behind finding the g(x,y) function as it looks like it uses the idea that to rotate a function around the origin you replace x with xcos(A)-ysin(A), but I am unsure about how the x-sin(a) and dividing the whole equation by cos(A) changes how to function works.
I made that video quite a while ago now and I have lost the algebra that I did to build what was going on. I recall that the equation in desmos that you see is a simplification of many lines of code and that is what it came out to so that it could be done in one line instead of many. However, this file was an earlier version that might be more instructive for how it works to rotate a function by manipulating the variables. www.desmos.com/calculator/gtdg39ojud
Hello, I'd really like some help in this matter. So I have gotten the rotated function, but it is in terms of G(x,y). how do i integrate this function (the function is only a 2d function yet it has 2 variables)
try "y=g(x,y)"
oh wait thats not what you're asking sorry
@@ianyourgod exactly lol. I have tried researching and asking many people about this and they have been confused
@@hriday7185 I think how it works is that you pass in an x and a y and then you see if the y you passed is equal to the thing that you got returned
Perhaps this will help: th-cam.com/video/V7ZSQUHAYRo/w-d-xo.html
Hi, just a quick question, can you have this series of equations appear on the same document more then once or should it need some changed variables to adjust? I can't see to make two lines with the series of equations used in the first link of the description.
Try using this method instead. I used capital X and Y to do the rotation, but you could easily add lines defining any other corresponding variables to rotate a second equation. www.desmos.com/calculator/gtdg39ojud
May I ask how may one rotate a relation, with the same freedom as presented in this video?
There is a link to the desmos file I am using in the description and you can drag the slider on the left side to change the angle.
I was wondering how I could do this with a non function. The specific equation is sin^2(x)-sin^2(y)=0.99
Sorry it took me a while to get back to you. In order to rotate a graph like yours you should replace the x with xcosA - ysinA and replace the y with xsinA + ycosA where A is the angle that you want to rotate counterclockwise with the rotation centered at the origin. Here is a link to a graph doing this. Hope this helped. www.desmos.com/calculator/sjrdqyvgf4
how can I rotate an equation with it ennpoint?
That is going to be a little tricky. I will look into it.
Oh, when I looked into it, it should already work. Just attach the restriction to the end of the original equation like {x
@@mr.h.heretohelp6541 why thank u, u deserve to be known bigrespect to u
what if I want to set it to rotate around a different axes other than 0?
I really need to make a video of the changes to do that. It is the most common question that I get. Here is a desmos graph link of how... video will hopefully come soon. www.desmos.com/calculator/ldhfhkqgkw
Nifty ! How might you go about rotating around ANY point that is perhaps already following a curve ? I'd think you could just add to the x & y such as "y = g(x + p1.x, y + p1.y)" but something is not right.
I get this question often. Check out this small change to the file that should allow you to rotate around any point. Video coming soon. www.desmos.com/calculator/ldhfhkqgkw
I just describe the equation in parametric form, and multiply it by a unit complex number w, with my desired angle. Works like a charm. Doesn't work for implicits (not to my knowledge), though. I wrote my own complex number lib in Desmos kinda for this purpose.
Hi this equation worked really well for me, but I was wondering how you found out that xcosa-ysina and xsina-ycosa was what you had to replace x and y with to make a function rotate? Is there a derivation or was it mostly just guess and checking?
I can't derive it all in a comment but here is a link to a paper that does a fantastic job of it. math.sci.ccny.cuny.edu/document/Rotation+of+Axes#:~:text=Coordinate%20Rotation%20Formulas&text=x%20%3D%20%CB%86xcos%20%CE%B8%20%E2%88%92%20%CB%86y%20sin%CE%B8,x%20sin%CE%B8%20%2B%20y%20cos%20%CE%B8.
It's a bit late, but I think it is a rotation matrix.
Excuse me, how may I rotate a polar equation that is labeled as r=csc(6theta)+6? I have subscribed, and I thank you, Professor.
Replace theta with (theta +A) where A is the amount you would like to rotate counterclockwise.
@@mr.h.heretohelp6541 , many thanks!
Hello. This is super helpful in general, but I am in the middle of a project where I need to do this to one side of an inequality. I’m making a flame-shape and it moves along a sine function. I’m trying to make the flame “blow in the wind” essentially.
Excellent Sir. Salute to you.
Kamalakar B thanks. Let me know if there are other things you are interested in tutorials about.
How do you get the play of the angle on the screen?
Open the link in the description to the desmos file that I made for this and drag the slider on the left side labelled A_ngle.
How would I set this up if I wanted to reflect points or a function across any arbitrary line, say y=2x?
What is going on with the syntax for the s(x,y)=g(x,y{y=0}) line? I'm not sure I understand what it's supposed to do. When I change it, odd things show up. When I remove it, it doesn't seem to make a difference.
Good job noticing that line. I had left that in from when I was tinkering around trying to get it to work. It is not needed in the final version. What it was meant to do originally was to graph the function separately when y=0 whenever it would normally be undefined by replacing it with the g function. This wasn't needed in the end though and I just forgot to remove that line.
is there a way to do this for multiple functions individually?
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
Sir, just wanted to ask that is there a way to integrate a rotated sine function
Can you be more specific? I can't think of a method to do it in general.
How do rotate a formula that has a< symbol.
Just replace the x with (xcosA-ysinA) and replace the original y with (ycosA+xsinA) then make a slider for A. Using the A slider will rotate your original inequality.
So, this is great but how does it work?
Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
mine says s isnt defined
You may have a typo when putting in sinA. This happens sometimes if you have the s separated from the rest of the sinA function.
Hi sir! thank u for this video, but are we able to know the function after rotating the angle? I'm trying to find a function with the points that I have plotted
Not really, the closest you could get is looking at line 11 in the desmos file linked in the description. Most of the time, your rotation will no longer be a function of one-variable [it won't pass the vertical line test, so you can't always have it in the form y=f(x)]. But, look at line 11 and see if you can build an equation for what you need. Otherwise, check out my video on regressions and that may actually be more of what you need in your example.
I was thinking this over again and I think that I thought of a way to do it. Take your original equation, for example 3x+2y=5 and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
How do you enter an equation that is implicitly defined in your program? The way you have set it up makes the user enter an explicitly defined function.
The way I have it set up in desmos will only allow explicitly defined equations to be evaluated this way. I guess a more accurate title would be "How to Rotate an Explicitly Defined Function | Using Desmos." I can't think of initially how that would be done.
can i rotate an elipse?
ax^2+bx^2+cx+dy+e=0
Try changing the values of cx and dy in the equation, then you'll find them rotating.
sorry for the confusion, actually, changing those two just makes translation of the elipse. My answer is quite incorrect.
Take your original equation and replace the x with xcos30-ysin30 and replace the y with xsin30+ycos30 This should rotate the equation 30 degrees counter-clockwise and you will have a specific equation for doing so. Should work with any angle.
@@mr.h.heretohelp6541 wow! thank you for answering to my comment. I thought I wouldn't figure out how, but you responded. thank you again.
How can I rotate any equation in contingent to any point in desmos??
I added that feature to the graph after seeing your comment. Look in the description of the video. There is the original Desmos link and the new link named " *Rotate Any Equation Around Any Point.* "