Question

How do you solve `cos(x/2)=(sqrt 2 / 2)` in the interval 0 to 2pi?

Answer 1

`pi/2`

Explanation:

`cos(x/2)=(sqrt(2)/2)`

`cos(x/2)=cos(2kpi+-pi/4), k in RR`

`x/2=2kpi+-pi/4`

`x=4kpi+-pi/2`

So the solutions in `[0, 2pi]` is `pi/2`