how would u find all the solutions of 2cosx-1=0?

Question

can u explain the steps to find all the solutions? i have to put it in this format A+BkП (pi) and C+DkП (pii). thank u!

Answer 1

2cos(x) -1 = 0
2cos(x) = 1
cos(x) = 1/2
x=arccos(1/2) = pi/3 and 5pi/3 [over one complete cycle 0 to 2pi]
Since cos(x) is periodic, these solutions occur during 2pi period, so the solutions you are looking for are:
pi/3 + 2pi(n) and 5pi/3 + 2pi(n) where -infinity

Answer 2

ok, so you know that cosx = 1/2
if you draw the unit circle (or just look at it) you will see that there are two places that cos is 1/2. This is at 5pi/3 and at pi/3.