State the quadrant in which the terminal side of each angle lies.
1) 11pi/4
11pi/4 = 2pi + 3pi/4
looks like QII to me
To determine the quadrant in which the terminal side of an angle lies, we need to consider the value of the angle when it is represented in standard position (with its initial side along the positive x-axis and its vertex at the origin).
In this case, the angle is given as 11π/4.
To determine the quadrant, divide the angle by π/2 (or 90 degrees). The quotient will represent the rotation around the unit circle from the positive x-axis (initial side) to the terminal side of the angle.
Let's do the calculation:
11π/4 ÷ π/2 = 11π/4 × 2/π = 11/2
The quotient of 11/2 indicates that the terminal side of the angle lies in the 5th quadrant.
Therefore, the answer is: The terminal side of the angle 11π/4 lies in the 5th quadrant.