What function would be $\rm abs(\sin(x))$ over a circle (like flower petals)

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Imagine I have the equation of a unit circle. I wish to draw (programmatically) something similar to $\rm abs(\sin(x))$ running over and around the circumference.

Just like drawing the external "petals" of a flower.

How can I proceed to create this equation of a half sine wave going around the circle (it would be nice if it were a simple equation I could write in code)?

Would it be easier by using the complex plane? Which is probably more difficult to program?