I don't understand how sin(5pi/3)= -squareroot(3)/2 and not +squareroot(3)/2. 5pi/3 is equal 300degree. it is on the +x-axis so it exact value should be positive right?Explain.

Answer 1

5 pi /3 is 300 degrees indeed
that is 60 degrees BELOW the + x axis which is at 0 or 360
so x is positive and y is NEGATIVE
so the sin = y/x is negative

Answer 2

sin = y/r
y is negative
r is always positive