Final answer:
The terminal point determined by π-t is (-8/17, 15/17), by -t is (-8/17, -15/17), by π+t is again (-8/17, -15/17), and by 2π+t returns to the starting point (8/17, 15/17).
Step-by-step explanation:
The subject of the question involves determining the coordinates of a point on a unit circle after applying certain transformations. If the initial point determined by t on the unit circle is (8/17, 15/17), to find the terminal point for π - t, we reflect the point horizontally across the y-axis because subtracting from π corresponds to a half rotation around the circle. Thus, the new x-coordinate is the negative of 8/17 and the y-coordinate remains 15/17. Therefore, the coordinates become (-8/17, 15/17).
For the transformation -t, we rotate the point 180 degrees around the origin. This effectively changes the signs of both coordinates, resulting in (-8/17, -15/17).
With π + t, the point moves 180 degrees around the circle and continues in the direction indicated by t. This is equivalent to a reflection of the initial point across the origin, yielding the coordinates (-8/17, -15/17), the same as for -t.
Finally, for 2π + t, the point completes one full rotation and continues to t, so there is no change in the coordinates from the starting point, keeping it at (8/17, 15/17).