period of cos x

so basically i've got my first answer as 2pi/3 , substrate this from 2pi will give me the second angle which is 4pi/3 now keep adding 2pi to 2pi/3 or 4pi/3?does it really matter?

Add 2pi to both of them to get all the solutions.

yes, the solutions for 5x are 2pi/3 + 2pi, 4pi, etc. AND 4pi/3 + 2pi, 4pi, etc.

No. For tan, it's simpler: get your first solution by taking tan^-1, then just keep adding or subtracting multiples of 180.

Yes. But remember, you can subtract pi, 2pi, 3pi, etc. as well as adding them.

You have to do both to get the full range of solutions.

Still abit confusing knowing when to add and when to subtrac, for instance we've only done adding for the question we've been discussing apart from the part that 2pi-2pi/3=4pi/3

You will need to look at your situation and question and decide there, basically all your answers need to be in the range specified in the question, for some questions you'll only need to add, for others you'll only need to subtract, and for others you'll need to do both. If you're confused. Do both and then throw away all the ones that don't fit in your range.

That helped a lot thank you

No problemo, you'll get a hang of it once you practice a few questions, you'll be able to see exactly what you should right away.