Prompt 1:

Generate a Manim animation in the style of 3B1B to visually explain the definite integral of cos(x) and sin(x) from 0 to x, resulting in sin(x) and 1-cos(x) respectively.
1. Start with a unit circle
2. take a random point at angle x on the unit circle
3. show the position vector connecting origin to this point on the unit circle
4. construct a triangle with this position vector as hypotenuse, and 2 other sides with lengths = current x co-ordinate and y co-ordinate which are cosx and sinx respectively.
5. now take a small increment in the angle dx. show the corresponding change in the position from the point cosx, sinx to the point cos(x+dx), sin(x+dx) on the unit circle.
6. zoom into that arc length dx, and show in the limiting case, it basically becomes a straight line
7. consider this straight line as hypotenuse and show that it's sides are of lengths cosxdx and sinxdx.
8. cosxdx is the small vertical length, and sinxdx is the small horizontal length.
9. now show that how if we start from angle 0 and start incrementing our angle dx step by step to reach the final angle x, then the total length accumulated horizontally = 1 - cosx and the total length accumulated vertically = sinx.
Show each of these steps visually, i might have missed some information so feel free to fill the gaps, just make sure that it conveys the message beautifully, in a visually appealing way.
do not assume things, each time i prompted to you before for this, you gave me code that didn't rendered, meaning you obviously don't know much about the manim. Do web searches, if you are not confident about anything that you are using in the code, then just do a web search.


it was in agent mode, so the claude did all the terminal work, installation, commands and rendering. I got the video, but it had various issues.


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Prompt 2:

okay nice but it is supposed to be one complete video file.
the first scene (integralvisualisation) works, but has issues, for example that yellow vector is always the unit vector, and it's tip always lies on the unit circle we constructed, but clearly in the animation it's not, you are showing it's tip outside the unit circle and it moving, it moves along the unit circle bro. we shall see that red and green part and that lines inside the circle, also see the screenshot, there is just so much text overlapping and we aren't updating the screen when it should be. also completely remove the text "as we move along the unit circle: the red area represents ..... ".  also remove the "cosx" and "sinx" text.
make sure again that there is no text overlap anywhere, understand it's logic properly before starting to write the code.

the smallincrementvisualization.mp4 and accumulationvisualisation.mp4 files are completely meaningless, remove that completely and it's corresponding code.

focus mainly on the main part of the code. making sure that the first animation main video is rendered correctly, logically and visually.


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Prompt 3:

the current background is dark grey, make it pure dark.

the angle x 's text "x" sits on top of the yellow vector for some time, see the screenshot, later the line describing the "angle" doesn't feel natural and visually appealing, do yeah, handle that.

also, see the screenshot again, the green part is only supposed to be to the left of the (1,0) point and the tangent to it, but clearly there is still some to the right of that line too, maybe some bug. so fix that.

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Prompt 4:

i think the green area extending beyond x = 1 is bug. maybe rendering bug or something, maybe we need to think about the quality or frames or something.

completely remove the "visualizing integral cosxdx and sinxdx" text from the screen

the white line showing the angle extends beyond the vector and the x axis. it should simply connect the vector and the x axis, but there is that extra line for it.
you too know that's not natural, think what natural feels like here and make necessary changes.
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Prompt 5:

in this animation, we generate the red and green area by adding the lengths, incrementing the angle, seeing the correspoinding lengths and then stacking them up to get the area. the green lengths are always to the left of the line x = 1, so the area should always be to the left of this line, but you can clearly see that some of those lengths shows up to the right of that line. so please fix that issue. i think it occurs because when the angle is very small, then the lengths are just too small that they are shown both ways, or something like that, but most probably it's that small lengths at the beginning issue. fix that and run the command
source manim-env/bin/activate && manim -qh integral_visualization.py IntegralVisualization

to see if it actually renders and works.



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Prompt 6:
Okay, the current scene/video/animation (say scene1) is perfect, i'd like to add a new scene (or a clip), to the beginning of this video. basically, just show this video at the starting, then use some transition and show the current scene1 as it is.

move the yellow unit vector to the arbirary point on the unit circle, at angle x, then increment the angle dx, then zoom to that arc length to see the corresponding arc length dx, then show how when dx is smaller and smaller the arc length dx is a straight line, zoom square shouldn't be too small, but shouldn't be big enough to overlap with the elements of the circle.

show that if we see arc length dx as a hypotenuse and draw 2 sides to it, then it'll also have one angle as x, so it's sides will be cosxdx and sinxdx., understand internally which angle is exactly x in your zoomed version triangle, depending on where is the angle x, the corresponding side to it will be cosxdx and opposite will be sinxdx, the length and label of cosxdx should be red and that of sinxdx should be green.

make sure that the zoomed version looks clean and big enough and it doesn't have any overlapping with those sides or anything, just make it clean.

now this was for only one single step at angle x, animate it continuously as x increases. show these lengths in zoomed version for each step. handle the logic properly. we want to see how it relates to the integral.

it should be one complete video.  do not create seperate video files or make a script to render both videos at the same time. just make it into one video by default. it should be one continous animation. the animation should be detailed and slow, showing exactly what happens, it's very crucial that you understand exactly what we are animating here, it should be atleast 1 min video.
if already a class or function that does this exists, just remove it completely and implement it from scratch with the current instructions in mind.

finally run the animation using the terminal, by activating the environment ofc.

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Prompt 7:
do not mention anywhere the concept of area or text saying area. remove all the texts you just added. remove any labels or scenes text.

the zoomed diagram is exactly correct, i repeat again, the current diagram is exactly correct, however,
you mis labeled the lengths, the red line should be sinxdx and the green line should be cosxdx. Just mislabeling, so just fix that. do not make any other changes at all.
the box is way too big, it should be just at the top right corner of the screen. it shouldn't be that big. it should be like what is in the screenshot, use it for refernce.

i repeat again, the triangle is exactly correct right now, place it in the same position, cofiguration in this box as it was in the box before, but just a but smaller (like see the image), with updated labels.

remove all the explanatory texts that you just added. remove any labels or texts.

you moved the vector from angle x to again further angle x. move it from 0 to x. show it moving from 0 to x, not from x to further again x. max angle shouldn't be 90. this is very important.

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Prompt 8:
this is how it looks right now.
the zoomed square is way too big. it should be in the top right corner. and should feel like one isolated zoomed window that does not appear over any other elements of the scene.

the legs of triangle are touching the sides of the zoomed square.
show the lengths of triangle in the zoomed square changing for each length. don't just stop at your first step visual. show this zoomed arc length and it's corresponding triangle, sides for each angle from 0 to x.

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Prompt 9:

very nice.
the sides are mis labelled.

green length in the triangle inside zoomed box should be sinxdx and the red length should be cosxdx,
it's not about just the color, it's also the label. in other words, the horizontal side in that zoomed square's triangle should be sinxdx and the vertical side should be cosxdx.

place the updated cosxdx text to the right of the red side length, see the image, currently it looks like it's the label for the hypotenuse. move the label for this side length to the right side of the length, and the actual text label for the hypotenuse is at the bottom, when it should be just next to the hypotenuse. it should feel natural and intuitive.

also, on the unit circle, the arc length dx where you draw the square, that square looks out of place, see the image for what i mean, the arc length dx isn't even inside that box. so fix that.


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Prompt 10:

currently, in the next scene i.e. the scene where we show the area and integrals, there the red and green colors we are using are quite dry and less saturated. they should be exactly the same colored as the colors in our current demostration of arc length and cosxdx lengths and sinxdx lengths. the green area should have a proper green color and the red area should have a proper red color i.e. the green and red colors we're using in the first scene.

also, in the 2nd scene, where we show the integrals and the area stuff, there we draw a circle again, it shouldn't feel like that, instead, it should feel like we erased whatever there was in the first scene, and we just continued over it.