Question

if sin^-1(-1/2)=sin(x)=-1/2 , why is the the answer to sin^-1(-1/2)=pi/6 and not 11pi/6?

Answer 1

I don't understand the if part very well I think there may be some type-os there.
But in order for y=sin(x) to be one to one we need to restrict its domain.
Normally it has been chosen to restrict the domain from -pi/2 to pi/2
And this is what y=sin(x) looks like (sorta) there :
And you see y=sin(x) on [-pi/2,pi/2] is one to one and thereofere has a inverse function
normally called y=arcsin(x) or some people prefer the notation y=sin^{-1}(x)
And that graph looks like
Now as you notice 11pi/6 is not in the range of y=arcsin(x) therefore 11pi/6 cannot possible by an outcome from any value x of arcsin(x)
That is arcsin(x) doesn't equal 11pi/6 for any x