Question

How do you solve `1 - cos(x) = 1/2` from `[0,2pi]`?

Answer 1

`S = {pi/3, (5pi)/3}`

Explanation:

Isolate the cosine

`-cos(x) = 1/2 - 1`
`-cos(x) = -1/2`
`cos(x) = 1/2`

We know the cosine is `1/2` when we have `x = pi/3`, however, the cosine is also positive on the fourth quadrant, so another possible value of `x` is `x = 2pi - pi/3 = (6pi - pi)/3 = (5pi)/3`

Thus we have a set of solutions `S` such that `S = {pi/3, (5pi)/3}`