Question

how to solve sin ( theta + pi/2 ) = 1/2 ?

Answer 1

you remember the angle sum identity,
sin(x + y)=sin(x)cos(y) + cos(x)sin(y)

Answer 2

Using that for the sin(theta + pi/2) it will be the same as cos(theta)
so you get

\[\cos(\theta)=1/2\]

Answer 3

there are two angles where the cosine is 1/2...