Future suggestions from Susan

[ariel-phet]

Susan had the following future suggestions

(1) There is a difference in how multiple rotations between radians and degrees were depicted. In radians, it shows that it’s always 2pi more, while in degrees, it just does the calculation. Then, in radians, it moves from 5pi to 4pi + 7/6 pi. This is mathematically correct, but was very confusing for my student. I liked the degree version much better as it didn’t ‘give away’ that adding 2pi was the same angle.
(2) It would be really nice to be able to click all three graphs at one time – seeing how sin and cos make the tangent graph is challenging without that support
(3) It would also be great to show the tangent line on the unit circle (you can see an example here: https://www.mathsisfun.com/geometry/unit-circle.html )
(4) I would really strongly suggest we take this one step further and provide a way for students to connect equations to the graph to show changes related to amplitude, period phase shift, and vertical shifts. (Illuminations one was good but it is java based: https://illuminations.nctm.org/Activity.aspx?id=3589)

[amanda-phet]

There is a difference in how multiple rotations between radians and degrees were depicted. In radians, it shows that it’s always 2pi more, while in degrees, it just does the calculation. Then, in radians, it moves from 5pi to 4pi + 7/6 pi. This is mathematically correct, but was very confusing for my student. I liked the degree version much better as it didn’t ‘give away’ that adding 2pi was the same angle.

I can't track down a design decision explicitly outlining this, but I think the general idea was to display special angles in this way so they'd recognize 7π/6 (for example) and not need to do a calculation with fractions to see that 151/6 is the same as a multiple of π + 7/6. I am not worried about "giving away" the idea of an angle greater than 360º or 2π having the same trig values, since that is the goal of this sim.

It would be really nice to be able to click all three graphs at one time – seeing how sin and cos make the tangent graph is challenging without that support

This would require some redesign since these radio buttons change the values, the unit circle representation, and the graph representation. We'd need to figure out how to handle this in the Values accordion box and on the unit circle.

It would also be great to show the tangent line on the unit circle (you can see an example here: https://www.mathsisfun.com/geometry/unit-circle.html )

I think this would be really great, and not hard to add, but again would require some design time.

I would really strongly suggest we take this one step further and provide a way for students to connect equations to the graph to show changes related to amplitude, period phase shift, and vertical shifts. (Illuminations one was good but it is java based: https://illuminations.nctm.org/Activity.aspx?id=3589)

This seems like a separate screen, IMO.

@kathy-phet can you let me know if you think it would be ok to pursue some of these design changes?

[amanda-phet]

@kathy-phet and I discussed this

(1) To address this goal, we would like to change how 3π, 5π, etc. are displayed. To address the confusion, we should labels those as 2π + π, 4π + π, etc. rather than simplifying those values.

(2) This would require substantial design time, although we think it's possible to fit all three function values in the Values accordion box, and all three graphs could fit at the same time. We'd like to defer this for now.

However, a simpler redesign to support this goal would be to add legend icons next to the function radio button labels (colored lines).

(3) We love this idea, but it also feels like something that should go as a separate tangent view, and/or something in the preferences (e.g. "Right Triangle Trig"). Defer for now.

(4) This sounds like a separate "transformations" sim, which could be great, but not appropriate for the scope of this publication.

@jessegreenberg can you go ahead and make the changes described in (1) and (2)?

[jessegreenberg]

These are done, @amanda-phet can you please make sure 1 is working correctly and comment on improvements for 2?

For 1 - The easiest way to do this was to use a string for this custom representation. For negative angles, it looks something like -2pi - pi. However, you might notice the second floating minus sign is rendered a bit smaller by the browser. It is most noticeable if you compare it to the "minus sign" drawn by a fraction Node (a custom Line). If this is bothersome enough let me know and Ill spend some time making the minus signs all identical.

For 2 - It looks like this, any layout adjustements or anything else?

[amanda-phet]

All of this seems to be working well to me!

The only time I noticed the weird minus sign was when the point is at (-1,0):

All other angles look like this to me:

My preference would be to keep these consistent if possible, and with the larger sign (I think it's technically an m-dash). If it's a lot of work then we can leave it as it is.

[jessegreenberg]

I wasn't aware of em dash thanks! That did look better, but wasn't quite the same as the custom line drawn by the fraciton Nodes. I ended up changing this so that it uses FractionNode instead. Is there anything else needed for this issue?