Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference.

To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle 1 I would like to render lines from the center of the circle to 5 different points along the circumference between angle 0 and 1. There might be any number of points in between these two angles.

How can I calculate these 5 points? I would need to calculate the (x, y) using angle i and the (x, y) using angle i+1. and then get the arc between these two points.

How is this done and how would I then get the individual points within this arc so that I can incrementally draw lines from the center to these individual points?

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For circles around $(0,0)$ with radius $r$, the point $(x,y)$ on the circumference at angle $\varphi$ is $$(x,y) = (r\cos\varphi, r\sin\varphi) \text{.}$$