How to Rotate a Function | Using Desmos

This video shows how to rotate a function using the desmos online graphing calculator. Rotating an equation can be a challenge to do by hand but it is made much easier with Desmos.

Here is the link to the graph in the video:

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How to Rotate Any Equation Around Any Point:
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[gopats]

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.

[sirmexicanelmo]

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

[hriday]

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)

[mynt]

How would I set this up if I wanted to reflect points or a function across any arbitrary line, say y=2x?

[Gordy-iosb]

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.

[realcygnus]

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.

[kaydenl]

The sin graph rotated makes an unfortunate shape lol

[hotdogmech]

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?

[sibbyeskie]

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?

[lucasborage]

what if I want to set it to rotate around a different axes other than 0?

[Rgy]

Where the *INTERNAL CALCULATION* Link 1:53

[heathercrisp]

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.

[hillbilly]

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.

[o.om.m]

How do you get the play of the angle on the screen?

[chicoandreolaguer]

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.

[RobertLamar]

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.

[dde]

Sir, just wanted to ask that is there a way to integrate a rotated sine function

[athirahdayana]

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

[chicoandreolaguer]

May I ask how may one rotate a relation, with the same freedom as presented in this video?

[rowantwine]

is there a way to do this for multiple functions individually?