What is the exact value of sin(-15 degrees)?

Answer 1

Start with the anti-symmetry of sine
sin(x)=-sin(-x)
so sin(-15°)=-sin(15°)
Now use
cos²(x)-sin²(x)=cos(2x)
cos²(x)+sin²(x)=1
Subtract first equation from second:
2sin²(x)=(1-cos(2x))
sin(x)=sqrt((1-cos(2x))/2)
Put x=-15°
sin(15°)
=-sin(15°)
=-sqrt((1-cos(30°))/2)
=-sqrt((1-sqrt(3)/2)/2)