Cos(x/2) = -1/2?

Question

Trig is not my thing. Can someone please help me solve this question with step by step instructions please.
x is a real nuber such that 0 <=x<2pi

Please no snide comments I have not been in school for 8 years and now I am just starting my degree. I really appriciate the help as University notes supply questions with answers but not how to arrive at the solution. Thus my challenge is trying to figure out method.

Answer 1

(x/2) = (2π/3) , (4π/3)
x = 4π/3 , x = 8π/3
x = 4π/3 for 0 < x < 2π

Answer 2

Without using a calculator, you know that the cosine is negative when in quadrants 2 and 3. Cos(60) = 1/2,
so, (x/2) = 120 degrees or 240 degrees or 480 degrees or 600 degrees (it keeps going)

So, x = 240, or 480, or 960, or 1200, etc.

Of these, the only one that is between 0 and 360 is the 240 angle. I think this is the same as 7/6 Pi radians.

Answer 3

cos(x/2) = -1/2

Let u = x/2

cos(u) = -1/2

Using the unit circle, we find that:
u = 2pi/3, 4pi/3

So
x/2 = 2π/3
or
x/2 = 4π/3

Multiply both sides by 2:
x = 4π/3
or
x = 8π/3

Answer 4

normally, with all angles in degrees,
cos (60) = 1/2
and cos (180 - 60) = -1/2
or cos (120) = -1/2
x/2 = 120
x = 240 degrees

Answer 5

calculator:

radian mode

shift cos -1/2 = 2.094

x = 2.094 * 2 = 4.188

how you are going to write that is your problem ^.^