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The image presents a mathematical exercise involving a function \( f \), its inverse, and various related properties. The task appears to be broken down into several parts. Let's break it down and approach each problem systematically:

### Given Function:
The function is defined as:
\[
f(x) = \frac{1}{\sin x}, \quad \text{for } x \in ]0, \pi[
\]
### Questions and Solutions:

1. **Étudier la fonction \( f \) et construire sa courbe représentative dans un repère orthonormé.**
  

Soit f la fonction définie sur ]0, π[ par: f(x) = 1/sin(x). Étudier la fonction f et construire sa courbe représentative. Montrer que la restriction g de f possède une fonction réciproque g^{-1}. Montrer que sin(y) = 1/x et que cos(y) = √(x^2 - 1)/x.

Explore the study of the function f(x) = 1/sin(x), including its graphical representation, the calculation of its inverse, and the derivation of trigonometric identities such as sin(y) = 1/x and cos(y) = √(x^2 - 1)/x. This exercise is suitable for undergraduate-level mathematics.

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