Question

Find all real numbers to satisfy equation? sin(πx)=1/2

Answer 1

`x= 1/6+-2n, 5/6+-2n` where `n ∈ Z`

Explanation:

`sin(pix)=1/2`

Let `pix` be `u`:
`sin(u)= 1/2`

`u= pi/6+-2pin, (5pi)/6+-2pin`

Now replace `u` with `pix` and solve for `x` by dividing by `pi`:

`pix= pi/6+-2pin, (5pi)/6+-2pin`

`x= 1/6+-2n, 5/6+-2n` where `n ∈ Z`

graph{sin(pix)-1/2 [-10, 10, -5, 5]}