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We are given that the terminal point determined by \( t \) on the unit circle is \( \left( \frac{3}{5}, \frac{4}{5} \right) \). We are asked to find the terminal points for the following values of \( t \):

### Part (a) \( \pi - t \)

On the unit circle, subtracting \( t \) from \( \pi \) reflects the point across the y-axis. This means the x-coordinate changes sign, while the y-coordinate remains the same.

So the terminal point for \( \pi - t \) is:
\[
\left( -\frac{3}{5}, \frac{4}{5} \right)
\]

### Part (b) \( -t \)

On the unit circle, changing \( t \) to \( -t \) reflects the point across the x-axis. This means the y-coordinate changes sign, while the x-coordinate remains the same.

So the terminal point for \( -t \) is:
\[
\left( \frac{3}{5}, -\frac{4}{5} \right)
\]

### Summary of Terminal Points
- \( \pi - t \) gives \( \left( -\frac{3}{5}, \frac{4}{5} \right) \)
- \( -t \) gives \( \left( \frac{3}{5}, -\frac{4}{5} \right) \)

Would you like any further clarifications or additional details?

Here are some related questions you might consider:
1. What happens to the coordinates when reflecting across the origin (i.e., for \( \pi + t \))?
2. How can we generalize the effect of adding or subtracting angles from \( t \) in different quadrants of the unit circle?
3. What are the coordinates of the terminal point when \( t = \frac{\pi}{2} \) or \( t = 2\pi \)?
4. Can you describe the relationship between sine and cosine when shifting angles by \( \pi \) or by multiples of \( \frac{\pi}{2} \)?
5. How does the Pythagorean identity \( \sin^2(t) + \cos^2(t) = 1 \) relate to terminal points on the unit circle?

**Tip:** On the unit circle, transformations involving \( \pi \) (like \( \pi - t \) or \( t + \pi \)) always correspond to flipping signs of coordinates (reflections) depending on the specific axis.

Suppose that the terminal point determined by t is the point (3/5, 4/5) on the unit circle. Find the terminal point determined by the following: (a) pi - t, (b) -t.

Learn how to determine terminal points on the unit circle for t, pi - t, and -t. This problem explores reflections across the x-axis and y-axis, applying fundamental trigonometric principles. Suitable for high school students in Grades 9-12.

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