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The question in the image asks to find the angle \( \theta \) where \( 0^\circ \leq \theta \leq 360^\circ \) such that \( \sin \theta = \frac{\sqrt{3}}{2} \). The angle should be entered in degrees, separated by a comma.

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find all angles \( \theta \) in the range \( 0^\circ \leq \theta \leq 360^\circ \) such that \( \sin \theta = \frac{\sqrt{3}}{2} \).

2. **Identify the Reference Angle**: 
   - \( \sin \theta = \frac{\sqrt{3}}{2} \) is a well-known value for trigonometric functions.
   - The reference angle for which \( \sin \theta = \frac{\sqrt{3}}{2} \) is \( 60^\circ \).

3. **Determine Quadrants**:
   - The sine function is positive in the **first** and **second** quadrants.
   - So, \( \theta \) could be in the first quadrant (where \( \theta = 60^\circ \)) or the second quadrant (where \( \theta = 180^\circ - 60^\circ = 120^\circ \)).

4. **Find All Possible Solutions**:
   - Therefore, the two angles that satisfy \( \sin \theta = \frac{\sqrt{3}}{2} \) are:
     \[
     \theta = 60^\circ, 120^\circ
     \]

### Final Answer:

- The angles are \( 60^\circ \) and \( 120^\circ \).

Would you like further details, or do you have any questions? Here are 5 related questions you might explore:

1. What are the solutions for \( \cos \theta = \frac{\sqrt{3}}{2} \) in the range \( 0^\circ \leq \theta \leq 360^\circ \)?
2. How do we find reference angles for other trigonometric functions?
3. Can we solve this problem using radians instead of degrees?
4. How does the unit circle help in solving trigonometric equations?
5. What are the general solutions for \( \sin \theta = \frac{\sqrt{3}}{2} \)?

**Tip:** Always remember that trigonometric functions repeat their values periodically. For sine and cosine, this period is \( 360^\circ \).

Find the angle θ where 0° ≤ θ ≤ 360° such that sin θ = √3/2.

Learn how to find the angles where sin θ = √3/2 within the range 0° to 360°. This problem involves key trigonometric concepts such as reference angles and the sine function. Suitable for students in Grades 9-12.

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