2sin (2x - pi/3) = - 1
sin (2x - pi/3) = - 1/2
Trig table and unit circle give 2 solutions for (2x - pi/3)
a. (2x - pi/3) = - pi/6 + 2kpi
2x = - pi/6 + pi/3 = pi/6 + 2kpi
x = pi/12 + kpi
k = 0 --> x = pi/12 ; k = 1 --> x = 13pi/12 ;
b. 2x - pi/3 = pi - (-pi/6) = (7pi)/6 + 2kpi
2x = (7pi)/6 + pi/3 = (9pi)/6 + 2kpi = (3pi)/2 + 2kpi
x = (3pi)/4 + kpi
k = 0 --> x = (3pi)/4; k = 1 --> x = (7pi)/4
Answers for (0, 2pi) -->
pi/12; (3pi)/4 ; (13pi)/12 ; (7pi)/4
Answers for (-2pi, 0)
(-23pi)/12; - (5pi)/4 ; - (11pi)/12 ; - (pi/4)
Note.
(-23pi/12) is co-terminal to (pi/12)
(-5pi)/4 is co-terminal to (3pi)/4
(-11pi)/12 is co-terminal to (13pi)/12
(-pi/4) is co-terminal to (7pi)/4
