Question

How do you solve `sin^2 (theta) = 1/2` ?

Answer 1

`theta= pi/4 +(kpi)/2`

Explanation:

`sin^2(theta)=1/2`

`sin(theta)=1/sqrt(2)=sqrt(2)/2 or sin(theta)=-1/sqrt(2)=-sqrt(2)/2`

`theta=pi/4+2kpi or theta=3pi/4+2kpi or`

`theta=5pi/4+2kpi or theta=7pi/4+2kpi`

If you trace these four solutions in the trigonometrical circle you will see that the four can be resumed in just one:

`theta= pi/4 +(kpi)/2`