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The problem asks to find the *principal value* of \(\arcsin(0.36)\), where all angle measures are in degrees.

### Step-by-step solution:

1. **Understanding the principal value of arcsin**: The principal value of the arcsine function, \(\arcsin(x)\), is the angle \(\theta\) such that \(-90^\circ \leq \theta \leq 90^\circ\). This range is chosen because it's where the sine function is one-to-one, ensuring a unique solution for \(\arcsin(x)\).

2. **Calculation of \(\arcsin(0.36)\)**:
   \[
   \theta = \arcsin(0.36) \approx 21.1^\circ
   \]

Thus, the principal value of \(\arcsin(0.36)\) is approximately **21.1°**.

### Answer:
The correct answer is **A) 21.1°**.

Would you like more details on this, or have any other questions?

Here are some related questions for further exploration:
1. What is the general solution for \(\arcsin(x)\) in degrees?
2. How does the range of arcsine differ from other inverse trigonometric functions?
3. What are the properties of the sine function in different quadrants?
4. How would you compute the sine of angles larger than \(360^\circ\)?
5. What is the difference between radians and degrees in trigonometry?

**Tip**: Remember that inverse trigonometric functions return specific values within their defined ranges to ensure uniqueness.

Which is the principal value of arcsin(0.36)?

Understand how to find the principal value of arcsin(0.36). This trigonometric problem highlights key concepts, including inverse trigonometric functions and the principal value range. Suitable for Grades 10-12.

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