Question

What point on the unit circle corresponds to -2π/3? A - (-√3/2, -1/2) B- (-√2/2, -√2/2) C- (-1/2, -√3/2) D- (-1,0)

Answer 1

`\text{The point corresponding to an angle}\ \alpha\ \text{ on the unit circle}\\\\\text{has the coordinates}\ (\cos\alpha,\ \sin\alpha).\\\\\text{We know}\ \cos(-x)=\cos(x)\ \text{and}\ \sin(-x)=-\sin(x).\\\\\cos\left(-(2\pi)/(3)\right)=\cos\left((2\pi)/(3)\right)=-\cos\left((\pi)/(3)\right)=-(1)/(2)\\\\\sin\left(-(2\pi)/(3)\right)=-\sin\left((2\pi)/(3)\right)=-\sin\left((\pi)/(3)\right)=-(\sqrt3)/(2)\\\\Answer:\ \boxed{C.\ \left(-(1)/(2);\ -(\sqrt3)/(2)\right)}`