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### Problem Setup:
Given the function \( f \) defined on \( ]0, \pi[ \) by \( f(x) = \frac{1}{\sin(x)} \).

#### 1.1) **Étudier la fonction f et construire sa courbe représentative (C) dans un repère orthonormé.**
   - **Study the function \( f \) and plot its graph in an orthonormal coordinate system.**

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Soit f la fonction définie sur ]0, π[ par: f(x) = 1/sin(x). Les sous-questions incluent l'étude de cette fonction, la construction de sa courbe, l'existence d'une fonction réciproque, et le calcul d'une intégrale en utilisant les résultats précédents.

Explore the study of the function f(x) = 1/sin(x), including graph construction, the existence of an inverse function, and calculating a definite integral using trigonometric identities and inverse functions. This problem involves key concepts from calculus and trigonometry, suitable for undergraduate students.

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