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 $y$ $$y^2 = 1-x^2$$ $$y = \pm \sqrt{1-x^2} = \pm \sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^2} = \pm \sqrt{0.25}$$ $$\therefore y = \pm \frac{1}{2} \approx \pm 0.5$$ $\therefore $ The coordinates are $(0.8660,0.5)\,$and$\,(0.8660,-0.5)$.
