Reference angle is the angle that is formed by the the terminal side of teh angle and the horizontal line or the x-axis. The reference angles of the different quadrants can be determined using the formula correspondingly:
Quadrant 1: RF = actual angle
Quadrant 2: RF = actual angle - 90 = actual angle - pi/2
Quadrant 3: RF = actual angle - 180 = actual angle - pi
Quadrant 4 : RF = actual angle - 270 = actual angle - 3/4 pi
The first thing to do is to determine the quadrants of each angle and then apply the formula:
a. 19 pi /4 = 855 deg = 2nd Q = 135 + 45 = 180 (correct)
b. 15 pi/4 = 675 deg = 4th Q = 315 + 45 = 360 (correct)
c. 7 pi/4 = 315 deg = 4th Q = 315 + 45 = 360 (correct)
d. 12 pi/4 = 540 deg = x axis = not correct
Answers are A, B and C.
