Explanation in desmos:
https://www.desmos.com/calculator/9wde7wmpk0
The red circle is the unit circle
The green circle turn has a radius of 0.5 and turn inside the red one.
It is centered around the point M((cos t)/2,(sin t)/2) as t goes from 0 to 2 pi
The equation of the green circle as a function of t is:
sqrt( (x-(cos t)/2)^2+(y-(sin t)/2)^2 )=1/2
Now we are looking for the intersection of the green circle and the line x=0. We set x=0 in the last equation
sqrt( (0-(cos t)/2)^2+(y-(sin t)/2)^2 )=1/2
this simplify to:
y(y- sin t)=0 y=sin t or y=0 (more detailed calculation in the desmos file)
We can ignore the trivial point (0,0) in the case y=0
So the point of intersection of the green circle and the line x=0 is the point (0,sin t)