Question

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

sin(3x)= -1/2

Answer 1

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........