Question

Find all real numbers to satisfy equation? 2sin(x/2)-1=0

Answer 1

`x= pi/3+-4pin, (5pi)/3+-4pin` where `n ∈ Z`

Explanation:

`2sin(x/2)-1=0`

Let `x/2` be `u`:
`2sin(u)-1=0`
`sin(u)= 1/2`

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

Now replace `u` with `x/2` and solve for `x` by multiplying by `2`:

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

`x= pi/3+-4pin, (5pi)/3+-4pin` where `n ∈ Z`

graph{2sin(x/2)-1 [-3.04, 16.96, -5.08, 4.92]}