Question: From Unit Circle Trigonometric Animation to a Dynamic Complex Plane Visualization ( 𝑒 𝑖 )?

Hi,

I’m trying to transpose an existing animation that connects the unit circle to the graphs of cos⁡(θ)\ and sin⁡(θ)\ into a complex-numbers visualization, so that students can clearly see the link between

z=eiθ=cos⁡θ+isin⁡θ,arg⁡(z)=θ,∣z∣=1

and the corresponding real/imaginary components.

Goal: a dynamic view where a point z(θ) moves on the unit circle in the complex plane while (simultaneously)

• the projections show ℜ(z)=cos⁡θ\  and ℑ(z)=sin⁡θ,

•  the graphs of cos⁡θ and sin⁡θ are traced against θ\,

• and/or the angle θ\ and argument are displayed in a clean, didactic way.

To better illustrate my objective, here is the link to the target animation I would like to transpose: 

Illustration

Thank you in advance for your insights and feedback.

Animation_Question.mw