Answer
$(-0.8660,0.5), (-0.8660,-0.5)$
Work Step by Step
The line $x=-\frac{\sqrt{3}}{2}$ intersects the circle $x^2+y^2=1$ at $(-0.8660,0.5)\,$and$\,(-0.8660,-0.5)$ as can be seen from the figure.
The solution can also be obtained analytically by substituting $x=-\frac{\sqrt{3}}{2}$ in the equation $x^2+y^2=1$ and solving for $y$ $$y^2 = 1-x^2$$ $$y = \pm \sqrt{1-x^2} = \pm \sqrt{1-(-\frac{\sqrt{3}}{2})^2} = \pm \sqrt{0.25}$$ $$\therefore y = \pm \frac{1}{2} = \pm 0.5$$ $\therefore $ The coordinates are $(-0.8660,0.5)\,$and$\,(-0.8660,-0.5)$.
