Alright, so I know to do this and that this is correct from years of precalc, etc. but I was never taught why. I want to know why and why this does not ALWAYS apply it seems.
When given this problem:
sin x = -1/2
you know that sin is negative in first and 2nd quadrants so the answer is 30 degrees in the terminal angle, so its 30 in the 3rd and 4th quadrants. This make the answer 210 and 330 degrees. I get that and that is what I have answered in past.
On certain equations however (like this one) you need to write:
210 +- 360n, 330 +- 360n
And it seems you do this however many answers you have. WHY do you write +- 360n? What is n, and why would you need to write 360?
Then with something like
4sin^2x = 3
I am more confused, as the answer is clearly 60 degrees, and it is positive, so I would think following these rules the answer would be
60 +- 360n, 120 +- 360n
But because there is a 4 coefficient originally it is
60 +- 360n, 120 +- 360n, 240 +- 360n, 300 +- 360n
Why does this happen?