Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\frac{\pi}{4}$. What are the coordinates of point $A$ ?
Enter an exact value or round to the nearest hundredth.

Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\frac{\pi}{4}$. What are the coordinates of point $A$ ?
Enter an exact value or round to the nearest hundredth.

Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\frac{\pi}{4}$. What are the coordinates of point $A$ ?
Enter an exact value or round to the nearest hundredth.
