The problem asks to find the coordinates of the point on the unit circle corresponding to the angle $P\left( -\frac{3\pi}{2} \right)$.

Step-by-Step Solution:

1. Interpret the angle:
   The angle $-\frac{3\pi}{2}$ is a negative angle, so it is measured in the clockwise direction.

   To find the equivalent positive angle, we can add $2\pi$ to $-\frac{3\pi}{2}$: $-\frac{3\pi}{2} + 2\pi = \frac{\pi}{2}$ This means $-\frac{3\pi}{2}$ is coterminal with $\frac{\pi}{2}$, which corresponds to the positive y-axis on the unit circle.

2. Determine the coordinates:
   The angle $\frac{\pi}{2}$ points directly upwards on the unit circle. The coordinates of this point on the unit circle are: $(x, y) = (0, 1)$

Therefore, the coordinates of the point corresponding to $P\left( -\frac{3\pi}{2} \right)$ are $\boxed{(0, 1)}$.

Would you like more details on how unit circle coordinates are derived or have any further questions?

Related Questions:

1. What are the coordinates of the point at $P\left( \frac{\pi}{2} \right)$?
2. What is the significance of coterminal angles on the unit circle?
3. How do you find the coordinates of $P\left( \frac{3\pi}{2} \right)$?
4. How do negative and positive angles relate on the unit circle?
5. What are the sine and cosine values of $\frac{\pi}{2}$?

Tip: Remember that coterminal angles have the same terminal point on the unit circle, meaning their coordinates are identical!