Final answer:
The angle 15π/4 lies in the second quadrant, as it is equivalent to 3π/4 radians after reducing multiples of 2π, and 3π/4 radians falls between π/2 and π which is the range of the second quadrant.
Step-by-step explanation:
To determine the quadrant in which the angle 15π/4 lies, let's start by simplifying it. The angle can be converted into a more familiar form by recognizing that one full revolution around a circle is 2π radians. Therefore, 15π/4 can be seen as 3 full revolutions (since 3 * 2π = 6π) plus an extra 3π/4, which is equivalent to the angle 3π/4 after the three revolutions have been completed.
Knowing that a full revolution does not change the quadrant, we only need to find out the quadrant of the reduced angle 3π/4. The angle 3π/4 is more than π/2 but less than π, thus it lies in the second quadrant. The quadrant sequence goes from the first quadrant (0 to π/2) to the fourth quadrant (3π/2 to 2π). Specifically, the second quadrant angles are between π/2 and π radians.