Question

How do you solve `sin(x/2)=sqrt2/2`?

Answer 1

`pi/2 + 4kpi`
`(3pi)/4 + 4kpi`

Explanation:

`sin (x/2) = sqrt2/2`
Trig table gives:
`sin x/2 = sqrt2/2` --> arc `x/2 = pi/4`.
Unit circle gives another arc x that has the same sin value:
`x/2 = pi - pi/4 = (3pi)/4`

a. `x/2 = pi/4 + 2kpi` -->
`x = (2pi)/4 + 4kpi = pi/2 + 4kpi`

b. `x/2 = (3pi)/4 + 2kpi`
`x = (6pi)/4 + 4kpi = (3pi)/2 + 4kpi`