Answer:
[tex]\frac{19\pi }{4} ,\frac{15\pi }{4},\frac{7\pi }{4}[/tex]
Step-by-step explanation:
The reference angle is the angle produced by the angle's terminal side and the horizontal line or the x-axis. The reference angles of the different quadrants may be calculated using the following formula:
- RF = actual angle in Quadrant 1
- RF = real angle - 90 = actual angle - pi/2 Quadrant 2:
- RF = real angle - 180 = actual angle - pi = quadrant 3
- RF = real angle - 270 = actual angle - 3/4 pi = quadrant 4
The first step is to identify the quadrants of each angle and then use the following 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)
