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The document appears to be a mathematical problem set from a course titled "L1 MIPC – S1 – Outils Mathématiques – Majeure Informatique 2024/2025" at Université Jean Monnet. It consists of a series of exercises on the study of functions, trigonometry, and calculus. Here is an overview of the exercises:

1. **Exercise 1**: Find the exact value of \( \cos(x) \) given \( \sin(x) = \frac{\sqrt{2} - \sqrt{6}}{4} \), and determine \( x \) by elimination from a given set of angles.
2. **Exercise 2**: Calculate \( \sin(9\pi/5) \) given \( \cos(9\pi/5) = \frac{\sqrt{5} + 1}{4} \), and find the exact values of \( \cos(\pi/5) \) and \( \sin(\pi/5) \).
3. **Exercise 3**: Simplify various trigonometric expressions.
4. **Exercise 4**: Express various real numbers in terms of \( \cos(x) \) or \( \sin(x) \).
5. **Exercise 5**: Solve trigonometric equations using the unit circle within the interval \( ]-\pi, \pi] \).
6. **Exercise 6**: Represent points on the unit circle that satisfy certain trigonometric inequalities.
7. **Exercise 7**: Solve trigonometric inequalities within the interval \( ]-\pi, \pi] \).
8. **Exercise 8**: Solve a quadratic equation in terms of \( \cos(x) \) within the interval \( ]-\pi, \pi] \).
9. **Exercise 9**: Determine the sign tables of various functions.
10. **Exercise 10**: Find the domain, differentiability, limits, derivative, and variation table for several functions.

If you want me to solve a specific exercise or explain a particular concept, please let me know!

### Would you like more details on one of these exercises? Here are some follow-up questions you might consider:
1. How do you determine the exact value of \( \cos(x) \) given \( \sin(x) \)?
2. What methods can be used to solve trigonometric equations on a unit

The document contains exercises from the course "L1 MIPC – S1 – Outils Mathématiques – Majeure Informatique 2024/2025" at Université Jean Monnet. It includes problems on trigonometry and calculus, such as finding exact values of trigonometric functions, solving trigonometric equations, simplifying expressions, and working with limits and derivatives.

This set of exercises from the course 'L1 MIPC – S1 – Outils Mathématiques – Majeure Informatique 2024/2025' covers trigonometric identities, solving trigonometric equations, simplifying expressions, and finding limits and derivatives of functions. Suitable for university-level students.

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