The cosine of an angle θ, defined on the unit circle, represents the x-coordinate of the point on the circle. Since \( \cos(\theta) = -\frac{1}{2} \), we can find the corresponding y-coordinate using the equation of the unit circle:
\[ x^2 + y^2 = 1 \]
Substituting \( x = -\frac{1}{2} \):
\[ \left(-\frac{1}{2}\right)^2 + y^2 = 1 \] \[ \frac{1}{4} + y^2 = 1 \] \[ y^2 = 1 - \frac{1}{4} \] \[ y^2 = \frac{3}{4} \] \[ y = \pm \frac{\sqrt{3}}{2} \]
Thus, the coordinates of the points on the unit circle where \( \cos(\theta) = -\frac{1}{2} \) are:
\[ \left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \quad \text{and} \quad \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right) \]
These points correspond to the angles \( \theta = \frac{2\pi}{3} \) and \( \theta = \frac{4\pi}{3} \) respectively.