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The image shows a mathematical problem involving the evaluation of a cosine function using a diagram of a unit circle. The problem is stated as follows:

- **Given function:** \( g(x) = \cos(x) \)
- **Task:** Evaluate \( g\left(\frac{\theta}{2}\right) \) using the information provided in the diagram.

### Interpretation of the Problem:

The diagram presents a unit circle with a point labeled \( (a, 1) \), and we are given an equation of the circle: 
\[
x^2 + y^2 = 5
\]
This represents a circle of radius \( \sqrt{5} \). We are to evaluate \( g\left(\frac{\theta}{2}\right) \), with the diagram suggesting that \( \theta \) corresponds to a specific angle in the circle.

The answer is given as:
\[
g\left(\frac{\theta}{2}\right) = \frac{\sqrt{10(5 - \sqrt{5})}}{10}
\]
This expression needs to be simplified and represents the result of evaluating the cosine function at a specific angle related to the diagram.

Would you like more detailed steps on how this result was derived from the unit circle and cosine function?

### Relative questions:
1. What does the equation \( x^2 + y^2 = 5 \) represent in a geometric context?
2. How can the angle \( \frac{\theta}{2} \) be determined from the diagram?
3. What role does the cosine function play in the context of the unit circle?
4. How would you simplify the given result, \( \frac{\sqrt{10(5 - \sqrt{5})}}{10} \)?
5. Can you describe the relationship between the coordinates of a point on the unit circle and the cosine function?

### Tip:
Remember that for any angle \( \theta \), the cosine of the angle corresponds to the x-coordinate of the point on the unit circle at that angle.

Use the figure to evaluate the following function, given that g(x) = cos(x). Evaluate g(θ/2) using the information provided in the diagram.

Learn how to evaluate the cosine function g(θ/2) using a unit circle diagram. This problem involves key trigonometric concepts such as the cosine function and radicals, with an equation x² + y² = 5 representing a circle of radius √5. Suitable for students in Grades 10-12.

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