https://file.aiquickdraw.com/mathbot/file/17254879813357dkv761k.jpg

The question in the image asks you to find the sine of the angle given in radians, \(-\frac{11\pi}{6}\).

To solve this:

1. **Identify the reference angle**:  
   \(-\frac{11\pi}{6}\) is in the fourth quadrant because when you add \(2\pi\) (full circle) to it, you get:
   \[
   -\frac{11\pi}{6} + 2\pi = -\frac{11\pi}{6} + \frac{12\pi}{6} = \frac{\pi}{6}
   \]
   This is equivalent to \( \frac{11\pi}{6} \), but the angle is in the fourth quadrant.

2. **Determine the sine of the reference angle**:  
   The reference angle for \(\frac{\pi}{6}\) is \(\frac{\pi}{6}\) itself.

   The sine of \(\frac{\pi}{6}\) is:
   \[
   \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}
   \]

3. **Adjust for the quadrant**:  
   Since the angle is in the fourth quadrant, the sine value is negative.

   Therefore:
   \[
   \sin\left(-\frac{11\pi}{6}\right) = -\frac{1}{2}
   \]

The correct answer is \(\boxed{-\frac{1}{2}}\).

Would you like further details or have any other questions?

Here are 5 related questions to explore further:
1. What is the cosine of \(-\frac{11\pi}{6}\)?
2. How would you find the tangent of \(\frac{7\pi}{4}\)?
3. What is the reference angle for an angle in the third quadrant?
4. How does the sine function behave for angles in the second quadrant?
5. Can you describe the process of converting an angle from degrees to radians?

**Tip:** When working with trigonometric functions, always consider the angle's quadrant to determine the sign of the result.

Find the sine of the angle in radians, -11π/6.

Learn how to calculate the sine of the angle -11π/6 using reference angles and the unit circle. This solution includes key trigonometric concepts and formulas suitable for students in Grades 10-12.

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