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The problem you're working on involves a unit circle and is asking for the coordinates of point \( Q \), which corresponds to an angle of \( -t \) radians, given the point \( P \) corresponds to an angle of \( t \) radians in standard position.

### Key Observations:
- On the unit circle, the coordinates of a point corresponding to an angle \( t \) are \( P = (\cos t, \sin t) \).
- The angle \( -t \) reflects point \( P \) across the x-axis.

### Solution for (a):
The coordinates of point \( Q \), corresponding to the angle \( -t \), will have the same x-coordinate as point \( P \), but the y-coordinate will be the negative of the y-coordinate of point \( P \).

Thus, the coordinates of \( Q \) are:
\[
Q = (\cos t, -\sin t)
\]

This matches the reflection of \( P = (\cos t, \sin t) \) across the x-axis, which gives \( Q = (x, -y) \).

Would you like further details or have any other questions?

Here are five related questions for further practice:
1. What are the coordinates of a point at an angle \( \pi/4 \) on the unit circle?
2. How would you find the coordinates of a point for an angle \( 2\pi - t \)?
3. What is the relationship between sine and cosine when reflecting across the y-axis?
4. Can you explain why the x-coordinate remains the same for reflections over the x-axis?
5. How does the unit circle help in understanding trigonometric identities?

**Tip:** The unit circle is a great way to visualize trigonometric functions. Understanding how the coordinates change with angle reflections will help in solving a variety of trigonometric problems.

What are the coordinates of the point Q corresponding to an angle of -t on the unit circle, given that the point P corresponds to an angle of t radians?

Explore how to find the coordinates of point Q on the unit circle when reflecting across the x-axis from an angle of t to -t. This problem involves trigonometric concepts such as the unit circle and reflections.

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