An observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point $(2,-2)$. Express the bearing using both methods.

Step 1 ：Given that the observer for a radar station is located at the origin of a coordinate system, we are to find the bearing of an airplane located at the point (2,-2).

Step 2 ：The bearing of an airplane can be calculated using trigonometric functions. It is the angle between the line from the observer to the airplane and the positive x-axis.

Step 3 ：The bearing can be expressed in two ways: true bearing and compass bearing.

Step 4 ：True bearing is measured in degrees clockwise from the north. To calculate true bearing, we first calculate the angle in standard position (counter-clockwise from the positive x-axis) and then convert it to a bearing (clockwise from the north).

Step 5 ：Compass bearing is expressed as a direction (N, S, E, W) and an angle. To calculate compass bearing, we first calculate the angle in standard position and then convert it to a compass direction and an angle.

Step 6 ：The coordinates of the airplane are (2, -2). This means the airplane is 2 units to the right and 2 units down from the observer.

Step 7 ：We can use the atan2 function to calculate the angle in standard position. The atan2 function returns a value in the range (-pi, pi), so we need to convert this to a value in the range (0, 2pi) by adding 2pi if the result is negative.

Step 8 ：Let x = 2 and y = -2. The angle in standard position is approximately 5.50 (in radians).

Step 9 ：Converting this to degrees, we get a true bearing of 135.0 degrees.

Step 10 ：Converting this to a compass bearing, we get E45.0 degrees.

Step 11 ：Final Answer: The true bearing of the airplane is \(\boxed{135^\circ}\). The compass bearing of the airplane is \(\boxed{E45^\circ}\).