give a general formula for all solutions. List 3 solutions

Question

sin(x/2)= -root3 /2

Answer 1

sinA=opposite side/hypotenuse = -root3/2 = -0.866

arcsin(-0.866) =- 60 degrees

or 300 degrees in quadrant IV,

or 240 degrees in quadrant III

the general solution is 240 degrees plus n(360) degrees where n is any integer

and 300 degrees plus n(360) degrees where n is any integer

so there are an infinite number of solutions. 240+360= 600 degrees for example

all solutions are in quadrants III or IV