The terminal point corresponding to an angle \( t = -\frac{\pi}{6} \) on the unit circle can be found as follows:

1. First, recognize that \( -\frac{\pi}{6} \) radians is equivalent to rotating \( \frac{\pi}{6} \) radians clockwise from the positive \( x \)-axis. 
2. \( \frac{\pi}{6} \) radians corresponds to 30 degrees, so we are rotating 30 degrees clockwise.
3. The reference angle is \( 30^\circ \), and the terminal point lies in the fourth quadrant.

Now, we calculate the coordinates of the terminal point using the unit circle:
- In the unit circle, for an angle \( \frac{\pi}{6} \), the coordinates are \( \left( \cos\left(\frac{\pi}{6}\right), \sin\left(\frac{\pi}{6}\right) \right) \).
- \( \cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2} \) and \( \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \).

Since the angle is in the fourth quadrant, the cosine remains positive and the sine becomes negative:
- Terminal point = \( \left( \frac{\sqrt{3}}{2}, -\frac{1}{2} \right) \).

Thus, the terminal point for \( t = -\frac{\pi}{6} \) is \( \left( \frac{\sqrt{3}}{2}, -\frac{1}{2} \right) \).

Would you like further clarification or more details on this? 

Here are 5 related questions to consider:
1. What is the terminal point for \( t = \frac{\pi}{3} \)?
2. How do you determine the reference angle for negative angles?
3. What is the terminal point for \( t = -\frac{\pi}{4} \)?
4. How are sine and cosine values affected by the quadrant in which the terminal point lies?
5. How would the terminal point change if \( t = -\frac{2\pi}{3} \)?

**Tip**: When dealing with angles in different quadrants, remember that sine and cosine take different signs depending on the quadrant.

Learn how to find the terminal point for t = -π/6 on the unit circle, using trigonometric concepts like reference angles and quadrants. This solution involves calculating cosine and sine values, with detailed explanations suitable for high school students (Grades 10-12).

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