An oscillator has an amplitude of 3.2. At this instant displacement of the oscillator is 1.4. What are the two possible phases of the oscillator at this instant?

Work so far:
x= Acos (constant)
x=displacement
A=amplitude

so
1.4=3.2 cos (constant)

.4375=cos(constant)

After that I am not sure what to do. Is my work even right or heading in the right direction?

You have it.

constant= arccos .4375

You should have in inverse buttion on your calculator.