When the problem asks to Find all solutions of the equation, I can solve the equation perfectly fine but i'm having trouble understanding when to use
kpi or 2kpi
4(cos^2(x)) - 1 = 0
cos(x) = Positive or Negative 1/2
well here is where I get confused as to how the answer should be and why.
Here is the way my teacher interpreted it for us: Since Cosine has a period of 2pi, we find all the radian measures where Cosine is 1/2 in the full circle or 2pi.
So I find : pi / 3, 2pi / 3, 4pi / 3, 5pi / 3.
This is the first part where I don't understand. According to the teacher, the answer should be all those plus 2kpi since Cosine has a period of 2pi.
Well the answers in the back of the book is claiming the answer is
(pi / 3) + kpi and (2pi/3) + kpi