Scaling of graphs seems inconsistent

[KatieWoe]

Test device
Samsung
Operating System
Win 11
Browser
Chrome
Problem description
For phetsims/qa#921
d/dx of sin(x) is cos(x) and d/dx of cos(x) is -sin(x). When you make a sin function on the Lab screen, and look at it's first and second derivatives, the shapes are right but either the amplitude or the scaling of the graphs seem inconsistent. Unless I am misremembering, when the three graphs are at the same level of zoom the lines should have the same amplitude. This is not the case in the default zooms. Additionally, if you adjust the zoom so that the sin and -sin graphs are equal amplitudes and make sure the cos graph is at the same zoom, it will still not have the same amplitude as the other two graphs.
Steps to reproduce

1. On the Lab screen, create a sin wave
2. Select the option to view the second derivative
3. Adjust the zoom of the second derivative graph so it is the same size as the sin wave
4. Adjust the zoom of the first derivative the same amount.

Visuals
These graphs at default zoom levels:

Adjusted:

What these three graphs should look like according to Desmos:

Troubleshooting information:

!!!!! DO NOT EDIT !!!!!
Name: ‪Calculus Grapher‬
URL: https://phet-dev.colorado.edu/html/calculus-grapher/1.0.0-dev.25/phet/calculus-grapher_all_phet.html
Version: 1.0.0-dev.25 2023-03-20 03:37:03 UTC
Features missing: applicationcache, applicationcache, touch
Flags: pixelRatioScaling
User Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/111.0.0.0 Safari/537.36
Language: en-US
Window: 1536x714
Pixel Ratio: 1.25/1
WebGL: WebGL 1.0 (OpenGL ES 2.0 Chromium)
GLSL: WebGL GLSL ES 1.0 (OpenGL ES GLSL ES 1.0 Chromium)
Vendor: WebKit (WebKit WebGL)
Vertex: attribs: 16 varying: 31 uniform: 4096
Texture: size: 8192 imageUnits: 32 (vertex: 32, combined: 64)
Max viewport: 8192x8192
OES_texture_float: true
Dependencies JSON: {}

[veillette]

Yes, that's an interesting observation. I wonder if we should rethink our scaling to get that effect. There is nothing incorrect per say in the simulation as the sinusoidal is not necessarily sin(x) but sin(k x) and that k will affect the derivative, which will become k cos(k x). The same thing applies to the second derivative. However, maybe we can set the default width, which is the wavelength, to be 2pi. However , we wanted to be consistent across all functions such that we would have by default a very wide parabola, triangles, etc.

[pixelzoom]

I don't have an opinion on this one, will defer to @veillette.

[veillette]

Currently the "width" of the parabola and the triangle (when the peak is at its half y max), matches the wavelength of the sinusoid

The current maximum wavelength is set to 5, and by default, (by having the slider set to the third tick is 3), whereas to have the effect that @KatieWoe proposed the wavelength by default should be 6.28 (2*pi).

One way around it is to have the width of the slider tune to half the wavelength, rather than the wavelength, this would bring us much closer to the effect that @KatieWoe was expecting.

[veillette]

There are two changes that need to be done to bring us to this effect.

• Changing the meaning of width for sine such that it matches the half-wavelength rather than the wavelength
• Start the slider at the mid-way position position.

(I turned on the values in the screenshot below to give you an idea of scale. I think @KatieWoe ' point was that it would be nice, if without values, and with the default setting, the derivative of the sine function would all have the same (nearly) amplitude.

[veillette]

Here is the patch if we want to go down that road.

Subject: [PATCH] change default values for sinusoid and slider position
---
Index: js/common/CalculusGrapherConstants.ts
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
diff --git a/js/common/CalculusGrapherConstants.ts b/js/common/CalculusGrapherConstants.ts
--- a/js/common/CalculusGrapherConstants.ts	(revision ff903f8238002dffe7764bb8ab46e98355947bcc)
+++ b/js/common/CalculusGrapherConstants.ts	(date 1679409735505)
@@ -75,7 +75,7 @@
   CURVE_MANIPULATION_WIDTH_RANGE: new RangeWithValue(
     0.1 * CURVE_X_LENGTH,
     0.5 * CURVE_X_LENGTH,
-    0.20 * CURVE_X_LENGTH ),
+    0.30 * CURVE_X_LENGTH ),
 
   // model height associated with curveManipulationDisplay (in the same unit as x-Range)
   CURVE_MANIPULATION_Y_RANGE: new Range( -0.25, TYPICAL_Y + 0.25 ),
Index: js/common/model/TransformedCurve.ts
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
diff --git a/js/common/model/TransformedCurve.ts b/js/common/model/TransformedCurve.ts
--- a/js/common/model/TransformedCurve.ts	(revision ff903f8238002dffe7764bb8ab46e98355947bcc)
+++ b/js/common/model/TransformedCurve.ts	(date 1679409568693)
@@ -480,7 +480,7 @@
     const closestPoint = this.getClosestPointAt( x );
 
     // Wavelength associated with the sinusoidal function
-    const wavelength = width;
+    const wavelength = width * 2;
 
     // Cosine function to apply to points. Cosine function passes through `position`
     const cosineFunction = ( x: number ) =>

[amanda-phet]

Thanks for bringing this up @KatieWoe

Discussed with @pixelzoom and @veillette and we'd like to divorce the width of the sine wave from the other curves, so we can have a default width of 2π.

[veillette]

In the commit above, the sinusoid wavelength/width is set to be 2pi by default.

With the default width value, we have

at the narrowest setting we have a couple of waves, enough to see the periodic behavior with multiple wavelengths..

and the widest is not so useful but I don't see any way around it.

[veillette]

I think this is a decent compromise. The students are more likely to use the default values in their exploration, and therefore I am not very worried about the usability at the very wide setting.

I'm assigning to @amanda-phet to review.

[amanda-phet]

This is looking great to me! This is a really good change. Closing this issue.