Question

Determine the angles if sin= -1/2

My answers were 11pie/6 and 4pie/3 ?

Answer 1

you should have an angle after the word sin
e.g. sinØ = -1/2

(without the angle it becomes a mathematical sin )

the reference angle is π/6, (because sin π/6 = +1/2 )

but your angle is in either quadrants III or IV
in III: Ø = π + π/6 = 7π/6
in IV: Ø = 2π - π/6 = 11π/6

one of your answers was correct, but
sin 4π/6 = .866...