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Devise three unique parametric expressions for a circle with a radius of ' r . ' These expressions should originate from the point ( 0

Devise three unique parametric expressions for a circle with a radius of $\'$ r $. \'$ These expressions should originate from the point $(0, -$ r $)$ and must meet the following conditions:

$($ a $)$ Complete one full rotation around the circle in a clockwise direction, returning to the point $(0, -$ r $) .$

$($ b $)$ Perform three complete rotations around the circle in a counter $-$ clockwise direction, ending at the point $(0, -$ r $) .$

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