In which quadrant does the terminal side of the angle 387° lie?

To calculate the terminal side of 387 we first reduce the angle to an angle smaller than 360 by factoring by 360
 So 387 = (360 * 1) + 27
 So 387 degrees lies in the same quadrant as 27 degrees.
 But 27 degrees lies between 0 and 90 degrees. Hence it follows that 387 lies in the first quadrant.