How to find an homeomorphism between $S^1$ and the image of a Cardioid

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I have to show an homeomorphism between the circle $S^1$ and the image of the Cardioid using this parametrization $$\gamma : \mathbb{R} \rightarrow \mathbb{R}^2\\ t \mapsto ((1-\cos(t))\sin(t) , (1-\cos(t))\cos(t)) $$ So I have to find an bijective application and prove that is an homeomorphism.