Final answer:
An angle of 315 degrees lies in the fourth quadrant.
Step-by-step explanation:
To determine the quadrant of an angle, we need to consider the reference angle. The reference angle for 315 degrees is 45 degrees. Since 45 degrees lies in the first quadrant, we can determine the quadrant of 315 degrees by using the rule that angles in the fourth quadrant have reference angles in the first quadrant.
The terminal side of a 315 degree angle lies in the fourth quadrant of the coordinate system. To understand this, we can visualize the coordinate plane divided into four quadrants. A full rotation around the coordinate plane is 360 degrees. So, an angle of 315 degrees starts at the positive x-axis (0 degrees) and moves in a counter-clockwise direction, completing just short of a full circle. Since 315 degrees is 45 degrees less than 360 degrees, it falls into the fourth quadrant, which is defined by positive x-values and negative y-values.