Use the exact values are given approximate solutions to three decimal places on the interval (0,2pi).

sin (3x) = - 1/2

Step-by-step explanation:

sin (3x) = - 1/2

general solution : sin (3x) = sin (-pi/6)

(3x = - pi/6 + 2kpi)

or

(3x = pi - (-pi/6) + 2k'pi)

x = - pi/18 + 2/3 kpi

or

x = 7pi/18 + 2/3 k'pi

solution in : (0,2pi)

k'=0 : x = 7pi/18

k' = 1 : x = 19pi/18

k' = 2; x = 31pi/18

k=0 : x = - pi/18 refused

k = 1 : continue ...