Trigonometrische Parametrisierung/Tangentialabbildung punktweise/Bijektiv/Aufgabe

Zeige, dass die Tangentialabbildung ${}T_{P}(\varphi )$ zu

\varphi \colon \mathbb {R} ^{1}\longrightarrow S^{1},\,t\longmapsto (\cos t,\sin t),

in jedem Punkt

{}P\in \mathbb {R}

bijektiv ist.

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