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The image contains points labeled \( P(x, y) \), and it seems that the problem is asking for the parameter \( t \), possibly in the context of parametric equations or trigonometric circles (e.g., on the unit circle). Based on the points given, this likely relates to the unit circle parameterization where \( x = \cos(t) \) and \( y = \sin(t) \).

Let's solve for \( t \) for each case:

### (a) \( P(0, 1), t = \)
- On the unit circle, \( \cos(t) = 0 \) and \( \sin(t) = 1 \). 
- This corresponds to \( t = \frac{\pi}{2} \) (90 degrees).

### (b) \( P\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right), t = \)
- Here, \( \cos(t) = -\frac{\sqrt{2}}{2} \) and \( \sin(t) = \frac{\sqrt{2}}{2} \).
- This corresponds to \( t = \frac{3\pi}{4} \) (135 degrees).

### (c) \( P(-1, 0), t = \)
- Here, \( \cos(t) = -1 \) and \( \sin(t) = 0 \).
- This corresponds to \( t = \pi \) (180 degrees).

### (d) \( P\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right), t = \)
- Here, \( \cos(t) = -\frac{\sqrt{2}}{2} \) and \( \sin(t) = -\frac{\sqrt{2}}{2} \).
- This corresponds to \( t = \frac{5\pi}{4} \) (225 degrees).

### (e) \( P(0, -1), t = \)
- Here, \( \cos(t) = 0 \) and \( \sin(t) = -1 \).
- This corresponds to \( t = \frac{3\pi}{2} \) (270 degrees).

### (f) \( P\left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right), t = \)
- Here, \( \cos(t) = \frac{\sqrt{2}}{2} \) and \( \sin(t) = -\frac{\sqrt{2}}{2} \).
- This corresponds to \( t = \frac{7\pi}{4} \) (315 degrees).

### Summary of values for \( t \):
- (a) \( t = \frac{\pi}{2} \)
- (b) \( t = \frac{3\pi}{4} \)
- (c) \( t = \pi \)
- (d) \( t = \frac{5\pi}{4} \)
- (e) \( t = \frac{3\pi}{2} \)
- (f) \( t = \frac{7\pi}{4} \)

Would you like more details or explanations for any of these? 

Here are 5 related questions to consider:
1. What is the general form of parametric equations for the unit circle?
2. How do sine and cosine values relate to angles in different quadrants?
3. What are the coordinates for common angles on the unit circle?
4. How can we convert between radians and degrees?
5. What is the significance of the unit circle in trigonometry?

**Tip:** Remember, radians are often used in trigonometry for simplicity and precision over degrees. One full circle corresponds to \( 2\pi \) radians.

Find the parameter t for each point P(x, y) on the unit circle.

Solve for the parameter t for points P(x, y) on the unit circle. This problem involves key trigonometric concepts such as cosine and sine functions and radians, and is ideal for students in Grades 9-12.

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