Draw an equilateral triangle. All sides and all angles are equal, so each angle is 180/3=60°.
Drop a perpendicular bisector from any vertex. This bisects the vertex angle making each half 60/2=30°.
The bisector also divides the opposite side into two equal halves.
The equilateral triangle is now split into two back-to-back right triangles. The sine of 30° is opposite/hypotenuse (you can apply this to both right triangles). The hypotenuse is simply the length of the side of the triangle, and the opposite is the bisected side, so it's half the length of the hypotenuse.
So (half the hypotenuse)/(hypotenuse)=½ exactly (or 0.5 in decimal).
But we need the sine of -30°. sin(-θ)=-sin(θ), so sin(-30°)=-½ (or -0.5).