# Unit circle wit sin in desmos

**URL:** <https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658>\
**Category:** Questions\
**Created:** [January 9, 2025, 4:20pm UTC](https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658 "2025-01-09T16:20:29Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Rebello](https://avatars.discourse-cdn.com/v4/letter/r/7ab992/32.png) [@Rebello](https://cl.desmos.com/u/Rebello)\
**Post date:** [January 9, 2025, 4:20pm UTC](https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658/1 "2025-01-09T16:20:29Z")

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Hello  
On Wikipedia you can find this animation:  
 ![Circle_cos_sin](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/c/c06fd6a5f798c5ac8eb37784d218a2f190916f4d.gif)  
I want to rebuild it like this:

 ![image](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/d/d5e87ced01305289f8aba60f4a9466639385f861.png)  
where you can use X\_1 to set the angle.

So I have an angle alpha which can be controlled by the point X\_1.

my current state is this:  
 ![desmos](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/3/36e8c0de7580f5386674f179b510893bdef35885.gif)

in the beginning everything is fine.  
But:  
When alpha gets over \pi/2, alpha doesn’t follow continuously along anymore.

I tried to rebuild the same project, to get new ideas on how to fix that. But now I am not able at all to make alpha work correctly. Not even for angles smaller than pi/2.

![desmos2](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/e/e2affbc1e401a5b700ee497d6283c74429795207.gif)

I dont want to restrict alpha to be between 0 and 2\pi.

[My project](https://www.desmos.com/calculator/jipucdpxrf)

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**Author:** ![Mike\_Gleeson](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/mike_gleeson/32/650_2.png) [@Mike\_Gleeson](https://cl.desmos.com/u/Mike_Gleeson)\
**Post date:** [January 9, 2025, 6:11pm UTC](https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658/2 "2025-01-09T18:11:37Z")

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Not entirely sure what you want but does this do? [Untitled Graph | Desmos](https://www.desmos.com/calculator/c5jst07lvf)

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<div class="post-metadata">

**Author:** ![Rebello](https://avatars.discourse-cdn.com/v4/letter/r/7ab992/32.png) [@Rebello](https://cl.desmos.com/u/Rebello)\
**Post date:** [January 9, 2025, 9:43pm UTC](https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658/3 "2025-01-09T21:43:22Z")

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thank you so much. I am missing this little angle in the triangle

 ![Bild_2025-01-09_214446870](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/9/94d0f96e27b82ed4774f5eb9a1f4244cca864ead.png)

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**Author:** ![Daniel\_Grubbs](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/daniel_grubbs/32/719_2.png) [@Daniel\_Grubbs](https://cl.desmos.com/u/Daniel_Grubbs)\
**Post date:** [January 9, 2025, 9:53pm UTC](https://cl.desmos.com/t/unit-circle-wit-sin-in-desmos/7658/4 "2025-01-09T21:53:10Z")

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Here you go. I edited @Mike_Gleeson’s [graph](https://www.desmos.com/calculator/igrwsdg80c) to include the arc.  
Two edits needed to display it properly you may not notice:

1. I confined the bounds of `a` from 0 to 2pi.
2. I changed `a` in the definition of `P` to a modular calculation. This allows you to continuously move the point in a circle, rather than stopping at 2pi and having to return back to 0 by rotating back clockwise.

(Edit: I initially had the arc from 0 rather than in the triangle. Fixed!)