# 2sin3x -1 = 0

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2sin3x -1 =0

Add 1:

==> 2sin3x = 1

Divide by 2:

==> sin3x = 1/2

But we know that sin pi/6 = 1/2

==> 3x = pi/6

Also we know that sinx is positive in 1st and 2nd quadrants:

==> 3x1 = pi/6 ==> x1= pi/18

==> 3x2 = pi-pi/6 = 5pi/6 ==> x2= 5pi/18

To solve 2sin3x - 1 = 0

2sin3x -1 +1 = 0+1

2sin3x = 1

sin3x =1/2 =sin 30 = sin (n*180+(-1)^n* 30) deg, n =0,1,2,...

3x = (180n+(-1)^n*30)/3 deg, n= 0, 1,2,...

x= (180n+(-1)^n30)/3 deg, n=0,1,2...

x = (60n+(-1)^n*10) deg, n= 0,1,2,3..

x= 10 , 50, 130, 170, 250, 290, 370 in deg etc