Simple trig question

[TonyHem]

Its "Find the first four positive solutions to the equation 2cos(3x-1)=1.2 to three decimal places"
Ive got the solutions, but I did something else first originally and I need to know why it's wrong, because its kind of how i've usually been doing things.






And from here, I added 2 pi to both of them for for 2 more solutions, +'ed 1 and divided by 3.

Originally I tried to, just have 0.927 + 1 then divide 3. That gave me 0.642 which is one solution. So i'm just wondering, why couldn't I do 2pi-theta ( the solution) to get the value inside the 4th quadrant? Or, even if I move the 1 over first making it 3x = 1.927, I can't seem to do 2pi-theta anymore. Is there a way to do it if I just solve for 1 x value first?

[kamil9876]

You have to be careful that when u add 1 u may be changing a negative number into a positive solution.

So you have:
3x-1=-0.927 
3x=0.927

and that's where the first positive solution comes from.

Basically, u want x>0

hence 3x>0

and 3x-1>-1

which -0.927 satisfies