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The image contains two mathematical exercises that involve evaluating trigonometric expressions at specific angles and finding the corresponding values.

### 1. **Problem 1: Evaluating \(\sin(2x + 1)\)**

This problem requires you to evaluate the sine function for different angles \(x\), where the values are typically given in degrees. The table shows the values of \(x\) along with the corresponding sine values.

To solve it:
- Calculate \(2x + 1\) for each given \(x\).
- Then, find the sine of the resulting angle.

### 2. **Problem 2: Evaluating \(\sin\left(\frac{7\pi}{4} + x\right)\)**

In this exercise, you need to evaluate the sine function for the expression \(\sin\left(\frac{7\pi}{4} + x\right)\) for specific values of \(x\).

To solve it:
- Add \(\frac{7\pi}{4}\) (which is equivalent to 315°) to the given angle \(x\).
- Then, find the sine of the resulting angle.

### Steps to Solve:
1. **Calculate the modified angle** using the provided formula in the expression.
2. **Evaluate the sine** of the angle obtained.

Would you like me to solve these steps for the provided angles in the table? Let me know if you need any details on trigonometric identities or how to find sine values from the unit circle!

Explore how to evaluate trigonometric expressions involving the sine function. Learn step-by-step methods to solve expressions like sin(2x + 1) and sin(7π/4 + x). This problem set covers key concepts in trigonometry and is suitable for advanced high school students.

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